{
    "cells": [
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "# Lesson 7: `groupby` and Indexing"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "## Objectives\n",
                "\n",
                "`pandas` is a very popular library used by data scientists to process **tabular data**: data organized into rows and columns like a spreadsheet. In this lesson, we'll discuss two key `DataFrame` operations: the `groupby` operation and the `apply` operation. We'll also discuss how `groupby` introduces an extra level of complexity towards indexing and slicing values. By the end of this lesson, students will be able to:\n",
                "\n",
                "* Explain in plain English the outcome of a `pandas` `DataFrame` `groupby` operation.\n",
                "* Apply the `groupby` operation to a `pandas` `DataFrame`.\n",
                "* Apply the `apply` operation to a `pandas` `DataFrame`.\n",
                "* Select values from a hierarchical index using tuples and the `slice` object as keys.\n",
                "\n",
                "\n",
                "## `groupby`\n",
                "\n",
                "Last time, we computed the \"shakiness\" of each location as the sum of all the magnitudes of earthquakes in that location across all time. For instructional purposes, let's review how to compute shakiness without `pandas` (using a list of dictionaries) and with `pandas` (using a `DataFrame`)."
            ]
        },
        {
            "attachments": {},
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Processing a List of Dictionaries\n",
                "For this problem, we want to process the `earthquakes.csv` as a list of dictionaries and return the result as a dictionary (where the keys are place names and the values are ShakeFactor)."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 23,
            "metadata": {},
            "outputs": [],
            "source": [
                "import cse163_utils"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 24,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "[{'id': 'nc72666881',\n",
                            "  'year': 2016,\n",
                            "  'month': 7,\n",
                            "  'day': 27,\n",
                            "  'latitude': 37.6723333,\n",
                            "  'longitude': -121.619,\n",
                            "  'name': 'California',\n",
                            "  'magnitude': 1.43},\n",
                            " {'id': 'us20006i0y',\n",
                            "  'year': 2016,\n",
                            "  'month': 7,\n",
                            "  'day': 27,\n",
                            "  'latitude': 21.5146,\n",
                            "  'longitude': 94.5721,\n",
                            "  'name': 'Burma',\n",
                            "  'magnitude': 4.9},\n",
                            " {'id': 'nc72666891',\n",
                            "  'year': 2016,\n",
                            "  'month': 7,\n",
                            "  'day': 27,\n",
                            "  'latitude': 37.5765,\n",
                            "  'longitude': -118.85916670000002,\n",
                            "  'name': 'California',\n",
                            "  'magnitude': 0.06},\n",
                            " {'id': 'nc72666896',\n",
                            "  'year': 2016,\n",
                            "  'month': 7,\n",
                            "  'day': 27,\n",
                            "  'latitude': 37.5958333,\n",
                            "  'longitude': -118.99483329999998,\n",
                            "  'name': 'California',\n",
                            "  'magnitude': 0.4},\n",
                            " {'id': 'nn00553447',\n",
                            "  'year': 2016,\n",
                            "  'month': 7,\n",
                            "  'day': 27,\n",
                            "  'latitude': 39.3775,\n",
                            "  'longitude': -119.845,\n",
                            "  'name': 'Nevada',\n",
                            "  'magnitude': 0.3}]"
                        ]
                    },
                    "execution_count": 24,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "# Using the code we wrote to parse the CSV to a list of dictionaries\n",
                "data = cse163_utils.parse('earthquakes.csv')\n",
                "data[:5]  # First 5 rows-- food for thought: how would we get the first five rows from a DataFrame?"
            ]
        },
        {
            "attachments": {},
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "To compute shakiness, we'll follow these steps:\n",
                "\n",
                "* Create a result dictionary\n",
                "* For each earthquake, find its `name` and `magnitude` and add the `magnitude` to the corresponding `name`.\n",
                " "
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 25,
            "metadata": {},
            "outputs": [
                {
                    "ename": "KeyError",
                    "evalue": "'California'",
                    "output_type": "error",
                    "traceback": [
                        "\u001b[31m---------------------------------------------------------------------------\u001b[39m",
                        "\u001b[31mKeyError\u001b[39m                                  Traceback (most recent call last)",
                        "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[25]\u001b[39m\u001b[32m, line 5\u001b[39m\n\u001b[32m      3\u001b[39m     name = earthquake[\u001b[33m'\u001b[39m\u001b[33mname\u001b[39m\u001b[33m'\u001b[39m]\n\u001b[32m      4\u001b[39m     magnitude = earthquake[\u001b[33m'\u001b[39m\u001b[33mmagnitude\u001b[39m\u001b[33m'\u001b[39m]\n\u001b[32m----> \u001b[39m\u001b[32m5\u001b[39m     \u001b[43mshakiness\u001b[49m\u001b[43m[\u001b[49m\u001b[43mname\u001b[49m\u001b[43m]\u001b[49m += magnitude\n\u001b[32m      7\u001b[39m shakiness\n",
                        "\u001b[31mKeyError\u001b[39m: 'California'"
                    ]
                }
            ],
            "source": [
                "shakiness = {}  # Empty dictionary\n",
                "for earthquake in data:\n",
                "    name = earthquake['name']\n",
                "    magnitude = earthquake['magnitude']\n",
                "    shakiness[name] += magnitude\n",
                "\n",
                "shakiness"
            ]
        },
        {
            "attachments": {},
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Uh-oh! We get a `KeyError` because we are trying to set values of a dictionary before we've initialized any keys! When using a `dict` as a counter, remember that we have to check for the key before trying to modify its value. Let's try again."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "{'California': 3638.4900000000084,\n",
                            " 'Burma': 22.200000000000003,\n",
                            " 'Nevada': 496.6400000000006,\n",
                            " 'Alaska': 3407.0000000000005,\n",
                            " 'Hawaii': 375.2099999999998,\n",
                            " 'Montana': 91.19000000000001,\n",
                            " 'Puerto Rico': 385.99999999999983,\n",
                            " 'Chile': 157.79999999999998,\n",
                            " 'Dominican Republic': 97.70000000000002,\n",
                            " 'British Virgin Islands': 230.09999999999994,\n",
                            " 'Indonesia': 298.60000000000014,\n",
                            " 'Washington': 176.2199999999999,\n",
                            " 'Southern East Pacific Rise': 15.799999999999999,\n",
                            " 'Argentina': 49.3,\n",
                            " 'Philippines': 85.19999999999999,\n",
                            " 'Canada': 99.96,\n",
                            " 'Papua New Guinea': 130.3,\n",
                            " 'Afghanistan': 43.6,\n",
                            " 'Oregon': 107.23000000000002,\n",
                            " 'South of Africa': 4.5,\n",
                            " 'Peru': 63.800000000000004,\n",
                            " 'Fiji': 75.0,\n",
                            " 'Japan': 192.60000000000002,\n",
                            " 'Oklahoma': 192.79999999999993,\n",
                            " 'Mexico': 111.45,\n",
                            " 'Kyrgyzstan': 39.8,\n",
                            " 'Tennessee': 36.24,\n",
                            " 'Tonga': 66.5,\n",
                            " 'Arkansas': 6.66,\n",
                            " 'South of the Fiji Islands': 77.00000000000001,\n",
                            " 'Utah': 71.59,\n",
                            " 'Georgia': 4.2,\n",
                            " 'U.S. Virgin Islands': 84.49999999999999,\n",
                            " 'Idaho': 27.930000000000003,\n",
                            " 'Wyoming': 46.29999999999999,\n",
                            " 'Iran': 13.299999999999999,\n",
                            " 'Syria': 4.4,\n",
                            " 'Russia': 122.60000000000001,\n",
                            " 'Tajikistan': 53.80000000000001,\n",
                            " 'Southwest Indian Ridge': 41.6,\n",
                            " 'Anguilla': 2.4,\n",
                            " 'Panama': 13.399999999999999,\n",
                            " 'Kansas': 47.489999999999995,\n",
                            " 'Northern Mariana Islands': 239.00000000000003,\n",
                            " 'Christmas Island': 5.0,\n",
                            " 'China': 63.900000000000006,\n",
                            " 'New Zealand': 88.40000000000002,\n",
                            " 'Vanuatu': 43.1,\n",
                            " 'Guatemala': 26.300000000000004,\n",
                            " 'Greece': 9.4,\n",
                            " 'Poland': 4.2,\n",
                            " 'Chagos Archipelago region': 4.4,\n",
                            " 'Italy': 64.3,\n",
                            " 'Virgin Islands region': 1.8,\n",
                            " 'New Jersey': 2.33,\n",
                            " 'Northern California': 2.45,\n",
                            " 'Southern Mid-Atlantic Ridge': 13.6,\n",
                            " 'South Sandwich Islands': 19.9,\n",
                            " 'South Georgia and the South Sandwich Islands': 99.7,\n",
                            " 'Northwest of Australia': 4.1,\n",
                            " 'South Indian Ocean': 26.900000000000002,\n",
                            " 'Solomon Islands': 45.5,\n",
                            " 'Mid-Indian Ridge': 4.9,\n",
                            " 'Portugal': 12.999999999999998,\n",
                            " 'Ascension Island region': 4.7,\n",
                            " 'Azerbaijan': 5.0,\n",
                            " 'India': 9.3,\n",
                            " 'Kiribati region': 4.6,\n",
                            " 'Martinique': 4.6,\n",
                            " 'Venezuela': 9.0,\n",
                            " 'Bolivia': 12.9,\n",
                            " 'Turkey': 8.0,\n",
                            " 'Vanuatu region': 4.5,\n",
                            " 'Missouri': 20.469999999999995,\n",
                            " 'Guam': 9.0,\n",
                            " 'Ohio': 1.98,\n",
                            " 'Nicaragua': 18.5,\n",
                            " 'East Timor': 4.5,\n",
                            " 'Northern Mid-Atlantic Ridge': 9.899999999999999,\n",
                            " 'Palau': 5.3,\n",
                            " 'Colorado': 19.4,\n",
                            " 'West Virginia': 2.31,\n",
                            " 'New Caledonia': 157.6,\n",
                            " 'Australia': 14.5,\n",
                            " 'Off the coast of Oregon': 7.199999999999999,\n",
                            " 'Virginia': 1.94,\n",
                            " 'Costa Rica': 17.7,\n",
                            " 'Ukraine': 4.8,\n",
                            " 'Colombia': 8.899999999999999,\n",
                            " 'East of the Kuril Islands': 4.7,\n",
                            " 'Cyprus': 4.1,\n",
                            " 'Pacific-Antarctic Ridge': 9.399999999999999,\n",
                            " 'Uzbekistan': 4.6,\n",
                            " 'Illinois': 7.289999999999999,\n",
                            " 'Central Mid-Atlantic Ridge': 4.3,\n",
                            " 'Western Indian-Antarctic Ridge': 4.5,\n",
                            " 'Ecuador': 8.5,\n",
                            " 'South of Panama': 4.6,\n",
                            " 'El Salvador': 9.399999999999999,\n",
                            " 'Western Xizang': 9.4,\n",
                            " 'Azores-Cape St. Vincent Ridge': 4.7,\n",
                            " 'North Carolina': 1.92,\n",
                            " 'North of Svalbard': 5.0,\n",
                            " 'Texas': 2.5,\n",
                            " 'Fiji region': 14.600000000000001,\n",
                            " 'Reykjanes Ridge': 4.5,\n",
                            " 'Arizona': 4.39,\n",
                            " 'Pakistan': 4.4,\n",
                            " 'Greenland Sea': 4.5,\n",
                            " 'New Hampshire': 1.5,\n",
                            " 'South Georgia Island region': 86.39999999999999,\n",
                            " 'New York': 1.48,\n",
                            " 'Central East Pacific Rise': 4.6,\n",
                            " 'North of Ascension Island': 9.5,\n",
                            " 'Pennsylvania': 1.37,\n",
                            " 'Japan region': 11.5,\n",
                            " 'Taiwan': 4.2,\n",
                            " 'Kuril Islands': 4.6}"
                        ]
                    },
                    "execution_count": 5,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "shakiness = {}  # Empty dictionary\n",
                "for earthquake in data:\n",
                "    name = earthquake['name']\n",
                "    magnitude = earthquake['magnitude']\n",
                "    if name not in shakiness:\n",
                "        shakiness[name] = 0\n",
                "    shakiness[name] += magnitude\n",
                "\n",
                "shakiness"
            ]
        },
        {
            "attachments": {},
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "And then we are done! It looks like California is the shakiest place on Earth!\n",
                "\n",
                "What we have just done is a **group by** operation on the data. We put all the earthquakes into groups *by* some column label such as `name`, *selected* column values of interest such as `magnitude`, and *aggregated* (by summing with `+`) the values in each group.\n"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "\n",
                "### Processing a `pandas` `DataFrame`\n",
                "Since group by is such a common operation, `pandas` has its own syntax. Understanding how the list of dictionaries approach works is a good starting point to understand what happens in the background when using `pandas`."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [],
            "source": [
                "import pandas as pd"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/html": [
                            "<div>\n",
                            "<style scoped>\n",
                            "    .dataframe tbody tr th:only-of-type {\n",
                            "        vertical-align: middle;\n",
                            "    }\n",
                            "\n",
                            "    .dataframe tbody tr th {\n",
                            "        vertical-align: top;\n",
                            "    }\n",
                            "\n",
                            "    .dataframe thead th {\n",
                            "        text-align: right;\n",
                            "    }\n",
                            "</style>\n",
                            "<table border=\"1\" class=\"dataframe\">\n",
                            "  <thead>\n",
                            "    <tr style=\"text-align: right;\">\n",
                            "      <th></th>\n",
                            "      <th>id</th>\n",
                            "      <th>year</th>\n",
                            "      <th>month</th>\n",
                            "      <th>day</th>\n",
                            "      <th>latitude</th>\n",
                            "      <th>longitude</th>\n",
                            "      <th>name</th>\n",
                            "      <th>magnitude</th>\n",
                            "    </tr>\n",
                            "  </thead>\n",
                            "  <tbody>\n",
                            "    <tr>\n",
                            "      <th>0</th>\n",
                            "      <td>nc72666881</td>\n",
                            "      <td>2016</td>\n",
                            "      <td>7</td>\n",
                            "      <td>27</td>\n",
                            "      <td>37.672333</td>\n",
                            "      <td>-121.619000</td>\n",
                            "      <td>California</td>\n",
                            "      <td>1.43</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>1</th>\n",
                            "      <td>us20006i0y</td>\n",
                            "      <td>2016</td>\n",
                            "      <td>7</td>\n",
                            "      <td>27</td>\n",
                            "      <td>21.514600</td>\n",
                            "      <td>94.572100</td>\n",
                            "      <td>Burma</td>\n",
                            "      <td>4.90</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>2</th>\n",
                            "      <td>nc72666891</td>\n",
                            "      <td>2016</td>\n",
                            "      <td>7</td>\n",
                            "      <td>27</td>\n",
                            "      <td>37.576500</td>\n",
                            "      <td>-118.859167</td>\n",
                            "      <td>California</td>\n",
                            "      <td>0.06</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>3</th>\n",
                            "      <td>nc72666896</td>\n",
                            "      <td>2016</td>\n",
                            "      <td>7</td>\n",
                            "      <td>27</td>\n",
                            "      <td>37.595833</td>\n",
                            "      <td>-118.994833</td>\n",
                            "      <td>California</td>\n",
                            "      <td>0.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>4</th>\n",
                            "      <td>nn00553447</td>\n",
                            "      <td>2016</td>\n",
                            "      <td>7</td>\n",
                            "      <td>27</td>\n",
                            "      <td>39.377500</td>\n",
                            "      <td>-119.845000</td>\n",
                            "      <td>Nevada</td>\n",
                            "      <td>0.30</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>...</th>\n",
                            "      <td>...</td>\n",
                            "      <td>...</td>\n",
                            "      <td>...</td>\n",
                            "      <td>...</td>\n",
                            "      <td>...</td>\n",
                            "      <td>...</td>\n",
                            "      <td>...</td>\n",
                            "      <td>...</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8389</th>\n",
                            "      <td>nc72685246</td>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>25</td>\n",
                            "      <td>36.515499</td>\n",
                            "      <td>-121.099831</td>\n",
                            "      <td>California</td>\n",
                            "      <td>2.42</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8390</th>\n",
                            "      <td>ak13879193</td>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>25</td>\n",
                            "      <td>61.498400</td>\n",
                            "      <td>-149.862700</td>\n",
                            "      <td>Alaska</td>\n",
                            "      <td>1.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8391</th>\n",
                            "      <td>nc72685251</td>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>25</td>\n",
                            "      <td>38.805000</td>\n",
                            "      <td>-122.821503</td>\n",
                            "      <td>California</td>\n",
                            "      <td>1.06</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8392</th>\n",
                            "      <td>ci37672328</td>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>25</td>\n",
                            "      <td>34.308000</td>\n",
                            "      <td>-118.635333</td>\n",
                            "      <td>California</td>\n",
                            "      <td>1.55</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8393</th>\n",
                            "      <td>ci37672360</td>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>25</td>\n",
                            "      <td>34.119167</td>\n",
                            "      <td>-116.933667</td>\n",
                            "      <td>California</td>\n",
                            "      <td>0.89</td>\n",
                            "    </tr>\n",
                            "  </tbody>\n",
                            "</table>\n",
                            "<p>8394 rows × 8 columns</p>\n",
                            "</div>"
                        ],
                        "text/plain": [
                            "              id  year  month  day   latitude   longitude        name  \\\n",
                            "0     nc72666881  2016      7   27  37.672333 -121.619000  California   \n",
                            "1     us20006i0y  2016      7   27  21.514600   94.572100       Burma   \n",
                            "2     nc72666891  2016      7   27  37.576500 -118.859167  California   \n",
                            "3     nc72666896  2016      7   27  37.595833 -118.994833  California   \n",
                            "4     nn00553447  2016      7   27  39.377500 -119.845000      Nevada   \n",
                            "...          ...   ...    ...  ...        ...         ...         ...   \n",
                            "8389  nc72685246  2016      8   25  36.515499 -121.099831  California   \n",
                            "8390  ak13879193  2016      8   25  61.498400 -149.862700      Alaska   \n",
                            "8391  nc72685251  2016      8   25  38.805000 -122.821503  California   \n",
                            "8392  ci37672328  2016      8   25  34.308000 -118.635333  California   \n",
                            "8393  ci37672360  2016      8   25  34.119167 -116.933667  California   \n",
                            "\n",
                            "      magnitude  \n",
                            "0          1.43  \n",
                            "1          4.90  \n",
                            "2          0.06  \n",
                            "3          0.40  \n",
                            "4          0.30  \n",
                            "...         ...  \n",
                            "8389       2.42  \n",
                            "8390       1.40  \n",
                            "8391       1.06  \n",
                            "8392       1.55  \n",
                            "8393       0.89  \n",
                            "\n",
                            "[8394 rows x 8 columns]"
                        ]
                    },
                    "execution_count": 7,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "df = pd.read_csv('earthquakes.csv')\n",
                "df"
            ]
        },
        {
            "attachments": {},
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "We first show how to do this in pandas, and then we will go back and explain what the syntax is saying."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "name\n",
                            "Afghanistan                         43.60\n",
                            "Alaska                            3407.00\n",
                            "Anguilla                             2.40\n",
                            "Argentina                           49.30\n",
                            "Arizona                              4.39\n",
                            "                                   ...   \n",
                            "Washington                         176.22\n",
                            "West Virginia                        2.31\n",
                            "Western Indian-Antarctic Ridge       4.50\n",
                            "Western Xizang                       9.40\n",
                            "Wyoming                             46.30\n",
                            "Name: magnitude, Length: 118, dtype: float64"
                        ]
                    },
                    "execution_count": 8,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "df.groupby('name')['magnitude'].sum()"
            ]
        },
        {
            "attachments": {},
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "The way to read this line of code uses the following logic:\n",
                "* `df` is the `DataFrame` we want to process\n",
                "* `.groupby('name')` tells the `DataFrame` we want it to group all of its rows **`by`** the `name` attribute. Conceptually, this step splits all the data into groups by `name`.\n",
                "* **For each group**, `['magnitude'].sum()` selects the `magnitude` from all rows in that group and aggregates the data by taking the `sum` of the rows.\n",
                "\n",
                "We can substitute `sum` aggregation operation for any other `Series` methods like `min`, `max`, and `mean`. You can also group by any column or use any column for your computations!\n",
                "\n",
                "The final result is a `Series` that uses the `name` as its index. Remember that most of the datasets we've seen had integer indices, but we noted that his was not always the case. The result of a groupby has the values you used for group (in this case the string names of locations) as the indices. This makes it convenient to find the shakiness of California specifically, for example."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "3638.4900000000084"
                        ]
                    },
                    "execution_count": 8,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "shakiness = df.groupby('name')['magnitude'].sum()\n",
                "shakiness['California']"
            ]
        },
        {
            "attachments": {},
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### What's going on here?\n",
                "It's pretty incredible that such a short line of code can do something so complex. In the bullet-list above, I described the steps that happen here but I find it easier to think about it with a small example. The figure below shows a visual explanation of what is going on when you do a `groupby`.\n",
                "\n",
                "1. **Teal, `data`**. Specify the `DataFrame`.\n",
                "2. **Purple, `.groupby('col1')`**. Call the `groupby` function on that `DataFrame` passing `col1` as the column for forming groups. This splits the data up into groups based on the provided column.\n",
                "    * This calls the `DataFrame.groupby(...)` method, **not** indexing with `[]`! Note the parentheses rather than square brackets.\n",
                "3. **Red, `['col2'].sum()`**. Specify the aggregation column, `col2`, and the aggregation function, `.sum()`. The values in each group are aggregated into a single value.\n",
                "    * This selects a particular column by indexing with `[]`.\n",
                "4. **Green, `result = `**. The final result evaluates to a `Series` with `col1` as the index and the aggregation value for each group.\n",
                "\n",
                "![Groupby Diagram, as explained by the numbered list above](groupby.png)\n",
                "\n",
                "To get better understand what's going on, let's freeze at step 3 (before aggregating results into a `Series`) to see how Pandas represents the `groupby` operation."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/html": [
                            "<div>\n",
                            "<style scoped>\n",
                            "    .dataframe tbody tr th:only-of-type {\n",
                            "        vertical-align: middle;\n",
                            "    }\n",
                            "\n",
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                            "\n",
                            "    .dataframe thead th {\n",
                            "        text-align: right;\n",
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                            "</style>\n",
                            "<table border=\"1\" class=\"dataframe\">\n",
                            "  <thead>\n",
                            "    <tr style=\"text-align: right;\">\n",
                            "      <th></th>\n",
                            "      <th>col1</th>\n",
                            "      <th>col2</th>\n",
                            "    </tr>\n",
                            "  </thead>\n",
                            "  <tbody>\n",
                            "    <tr>\n",
                            "      <th>0</th>\n",
                            "      <td>A</td>\n",
                            "      <td>1</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>1</th>\n",
                            "      <td>B</td>\n",
                            "      <td>2</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>2</th>\n",
                            "      <td>C</td>\n",
                            "      <td>3</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>3</th>\n",
                            "      <td>A</td>\n",
                            "      <td>4</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>4</th>\n",
                            "      <td>C</td>\n",
                            "      <td>5</td>\n",
                            "    </tr>\n",
                            "  </tbody>\n",
                            "</table>\n",
                            "</div>"
                        ],
                        "text/plain": [
                            "  col1  col2\n",
                            "0    A     1\n",
                            "1    B     2\n",
                            "2    C     3\n",
                            "3    A     4\n",
                            "4    C     5"
                        ]
                    },
                    "execution_count": 11,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "# Make a DataFrame by giving it a list of dictionaries\n",
                "example_data = pd.DataFrame([\n",
                "    {'col1': 'A', 'col2': 1},\n",
                "    {'col1': 'B', 'col2': 2},\n",
                "    {'col1': 'C', 'col2': 3},\n",
                "    {'col1': 'A', 'col2': 4},\n",
                "    {'col1': 'C', 'col2': 5},\n",
                "])\n",
                "\n",
                "example_data"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "<pandas.core.groupby.generic.DataFrameGroupBy object at 0x00000199CE7E4F50>"
                        ]
                    },
                    "execution_count": 12,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "groupby = example_data.groupby('col1') # Notice no aggregate\n",
                "groupby"
            ]
        },
        {
            "attachments": {},
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "This returns a special `pandas` object called a `DataFrameGroupBy`. This represents an \"unfinished\" `groupby` operation since we have not computed an aggregate yet. One feature that is kind of helpful for seeing what's going on (but you will probably rarely use in practice) is the fact you can loop over a `DataFrameGroupBy` to inspect the groups."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/html": [
                            "<div>\n",
                            "<style scoped>\n",
                            "    .dataframe tbody tr th:only-of-type {\n",
                            "        vertical-align: middle;\n",
                            "    }\n",
                            "\n",
                            "    .dataframe tbody tr th {\n",
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                            "\n",
                            "    .dataframe thead th {\n",
                            "        text-align: right;\n",
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                            "</style>\n",
                            "<table border=\"1\" class=\"dataframe\">\n",
                            "  <thead>\n",
                            "    <tr style=\"text-align: right;\">\n",
                            "      <th></th>\n",
                            "      <th>col1</th>\n",
                            "      <th>col2</th>\n",
                            "    </tr>\n",
                            "  </thead>\n",
                            "  <tbody>\n",
                            "    <tr>\n",
                            "      <th>0</th>\n",
                            "      <td>A</td>\n",
                            "      <td>1</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>3</th>\n",
                            "      <td>A</td>\n",
                            "      <td>4</td>\n",
                            "    </tr>\n",
                            "  </tbody>\n",
                            "</table>\n",
                            "</div>"
                        ],
                        "text/plain": [
                            "  col1  col2\n",
                            "0    A     1\n",
                            "3    A     4"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                },
                {
                    "data": {
                        "text/html": [
                            "<div>\n",
                            "<style scoped>\n",
                            "    .dataframe tbody tr th:only-of-type {\n",
                            "        vertical-align: middle;\n",
                            "    }\n",
                            "\n",
                            "    .dataframe tbody tr th {\n",
                            "        vertical-align: top;\n",
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                            "\n",
                            "    .dataframe thead th {\n",
                            "        text-align: right;\n",
                            "    }\n",
                            "</style>\n",
                            "<table border=\"1\" class=\"dataframe\">\n",
                            "  <thead>\n",
                            "    <tr style=\"text-align: right;\">\n",
                            "      <th></th>\n",
                            "      <th>col1</th>\n",
                            "      <th>col2</th>\n",
                            "    </tr>\n",
                            "  </thead>\n",
                            "  <tbody>\n",
                            "    <tr>\n",
                            "      <th>1</th>\n",
                            "      <td>B</td>\n",
                            "      <td>2</td>\n",
                            "    </tr>\n",
                            "  </tbody>\n",
                            "</table>\n",
                            "</div>"
                        ],
                        "text/plain": [
                            "  col1  col2\n",
                            "1    B     2"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                },
                {
                    "data": {
                        "text/html": [
                            "<div>\n",
                            "<style scoped>\n",
                            "    .dataframe tbody tr th:only-of-type {\n",
                            "        vertical-align: middle;\n",
                            "    }\n",
                            "\n",
                            "    .dataframe tbody tr th {\n",
                            "        vertical-align: top;\n",
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                            "\n",
                            "    .dataframe thead th {\n",
                            "        text-align: right;\n",
                            "    }\n",
                            "</style>\n",
                            "<table border=\"1\" class=\"dataframe\">\n",
                            "  <thead>\n",
                            "    <tr style=\"text-align: right;\">\n",
                            "      <th></th>\n",
                            "      <th>col1</th>\n",
                            "      <th>col2</th>\n",
                            "    </tr>\n",
                            "  </thead>\n",
                            "  <tbody>\n",
                            "    <tr>\n",
                            "      <th>2</th>\n",
                            "      <td>C</td>\n",
                            "      <td>3</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>4</th>\n",
                            "      <td>C</td>\n",
                            "      <td>5</td>\n",
                            "    </tr>\n",
                            "  </tbody>\n",
                            "</table>\n",
                            "</div>"
                        ],
                        "text/plain": [
                            "  col1  col2\n",
                            "2    C     3\n",
                            "4    C     5"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "for key, group in groupby: \n",
                "    display(group) # To get the fancy Jupyter Notebook display of table"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Alternatively, you can use the `.describe()` function, which gives several different summary statistics."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/html": [
                            "<div>\n",
                            "<style scoped>\n",
                            "    .dataframe tbody tr th:only-of-type {\n",
                            "        vertical-align: middle;\n",
                            "    }\n",
                            "\n",
                            "    .dataframe tbody tr th {\n",
                            "        vertical-align: top;\n",
                            "    }\n",
                            "\n",
                            "    .dataframe thead th {\n",
                            "        text-align: right;\n",
                            "    }\n",
                            "</style>\n",
                            "<table border=\"1\" class=\"dataframe\">\n",
                            "  <thead>\n",
                            "    <tr style=\"text-align: right;\">\n",
                            "      <th></th>\n",
                            "      <th>count</th>\n",
                            "      <th>mean</th>\n",
                            "      <th>std</th>\n",
                            "      <th>min</th>\n",
                            "      <th>25%</th>\n",
                            "      <th>50%</th>\n",
                            "      <th>75%</th>\n",
                            "      <th>max</th>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>col1</th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "    </tr>\n",
                            "  </thead>\n",
                            "  <tbody>\n",
                            "    <tr>\n",
                            "      <th>A</th>\n",
                            "      <td>2.0</td>\n",
                            "      <td>2.5</td>\n",
                            "      <td>2.121320</td>\n",
                            "      <td>1.0</td>\n",
                            "      <td>1.75</td>\n",
                            "      <td>2.5</td>\n",
                            "      <td>3.25</td>\n",
                            "      <td>4.0</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>B</th>\n",
                            "      <td>1.0</td>\n",
                            "      <td>2.0</td>\n",
                            "      <td>NaN</td>\n",
                            "      <td>2.0</td>\n",
                            "      <td>2.00</td>\n",
                            "      <td>2.0</td>\n",
                            "      <td>2.00</td>\n",
                            "      <td>2.0</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>C</th>\n",
                            "      <td>2.0</td>\n",
                            "      <td>4.0</td>\n",
                            "      <td>1.414214</td>\n",
                            "      <td>3.0</td>\n",
                            "      <td>3.50</td>\n",
                            "      <td>4.0</td>\n",
                            "      <td>4.50</td>\n",
                            "      <td>5.0</td>\n",
                            "    </tr>\n",
                            "  </tbody>\n",
                            "</table>\n",
                            "</div>"
                        ],
                        "text/plain": [
                            "      count  mean       std  min   25%  50%   75%  max\n",
                            "col1                                                  \n",
                            "A       2.0   2.5  2.121320  1.0  1.75  2.5  3.25  4.0\n",
                            "B       1.0   2.0       NaN  2.0  2.00  2.0  2.00  2.0\n",
                            "C       2.0   4.0  1.414214  3.0  3.50  4.0  4.50  5.0"
                        ]
                    },
                    "execution_count": 16,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "groupby['col2'].describe()"
            ]
        },
        {
            "attachments": {},
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "This is why when we do finish the computation, we get the sum of all these rows that fell into each group"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "col1\n",
                            "A    5\n",
                            "B    2\n",
                            "C    8\n",
                            "Name: col2, dtype: int64"
                        ]
                    },
                    "execution_count": 13,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "result = example_data.groupby('col1')['col2'].sum()\n",
                "result"
            ]
        },
        {
            "attachments": {},
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "It's important to highlight that **`result` is a `Series` with the step 2 group-by names as its index**. You can access the underlying `index` of a `Series` or `DataFrame` using its `.index` attribute."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "<class 'pandas.core.series.Series'>\n",
                        "Index(['A', 'B', 'C'], dtype='object', name='col1')\n",
                        "8\n"
                    ]
                }
            ],
            "source": [
                "print(type(result))\n",
                "print(result.index)\n",
                "print(result['C'])"
            ]
        },
        {
            "attachments": {},
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### When to use this?\n",
                "Whenever you want to separate your data into groups to get some value for each one, this is the natural time to ues a `groupby`! Whenever you see \"for each\" or \"per\" in a question, it's likely you will want to use a `groupby`. \n",
                "\n",
                "Here are some example questions you can solve with a groupby. We provide some \"code\" to compute each one, assuming the data had columns with the relevant names.\n",
                "* Compute the number of students per section\n",
                "    ```\n",
                "    grades.groupby('Section')['StudentID'].count()\n",
                "    ```\n",
                "* Compute the average grade of students in each section\n",
                "    ```\n",
                "    grades.groupby('Section')['Grade'].mean()\n",
                "    ```\n",
                "* Compute the total number of people in each country\n",
                "    ```\n",
                "    cities.groupby('country')['population'].sum()\n",
                "    ```"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "**Food for thought:** What would happen if we wanted to use `groupby` with multiple columns? For example:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/html": [
                            "<div>\n",
                            "<style scoped>\n",
                            "    .dataframe tbody tr th:only-of-type {\n",
                            "        vertical-align: middle;\n",
                            "    }\n",
                            "\n",
                            "    .dataframe tbody tr th {\n",
                            "        vertical-align: top;\n",
                            "    }\n",
                            "\n",
                            "    .dataframe thead th {\n",
                            "        text-align: right;\n",
                            "    }\n",
                            "</style>\n",
                            "<table border=\"1\" class=\"dataframe\">\n",
                            "  <thead>\n",
                            "    <tr style=\"text-align: right;\">\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th>count</th>\n",
                            "      <th>mean</th>\n",
                            "      <th>std</th>\n",
                            "      <th>min</th>\n",
                            "      <th>25%</th>\n",
                            "      <th>50%</th>\n",
                            "      <th>75%</th>\n",
                            "      <th>max</th>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>year</th>\n",
                            "      <th>month</th>\n",
                            "      <th>day</th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "    </tr>\n",
                            "  </thead>\n",
                            "  <tbody>\n",
                            "    <tr>\n",
                            "      <th rowspan=\"30\" valign=\"top\">2016</th>\n",
                            "      <th rowspan=\"5\" valign=\"top\">7</th>\n",
                            "      <th>27</th>\n",
                            "      <td>272.0</td>\n",
                            "      <td>1.617574</td>\n",
                            "      <td>1.095349</td>\n",
                            "      <td>0.06</td>\n",
                            "      <td>0.9000</td>\n",
                            "      <td>1.400</td>\n",
                            "      <td>2.0000</td>\n",
                            "      <td>5.60</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>28</th>\n",
                            "      <td>308.0</td>\n",
                            "      <td>1.448149</td>\n",
                            "      <td>0.896851</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.8775</td>\n",
                            "      <td>1.240</td>\n",
                            "      <td>1.8000</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>29</th>\n",
                            "      <td>309.0</td>\n",
                            "      <td>1.640129</td>\n",
                            "      <td>1.165952</td>\n",
                            "      <td>0.01</td>\n",
                            "      <td>0.8800</td>\n",
                            "      <td>1.450</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>7.70</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>30</th>\n",
                            "      <td>329.0</td>\n",
                            "      <td>1.615076</td>\n",
                            "      <td>1.262618</td>\n",
                            "      <td>0.03</td>\n",
                            "      <td>0.7000</td>\n",
                            "      <td>1.240</td>\n",
                            "      <td>2.0000</td>\n",
                            "      <td>5.70</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>31</th>\n",
                            "      <td>278.0</td>\n",
                            "      <td>1.750827</td>\n",
                            "      <td>1.261577</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.9000</td>\n",
                            "      <td>1.500</td>\n",
                            "      <td>2.1475</td>\n",
                            "      <td>5.90</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th rowspan=\"25\" valign=\"top\">8</th>\n",
                            "      <th>1</th>\n",
                            "      <td>356.0</td>\n",
                            "      <td>1.520056</td>\n",
                            "      <td>1.157326</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.8000</td>\n",
                            "      <td>1.245</td>\n",
                            "      <td>1.8025</td>\n",
                            "      <td>6.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>2</th>\n",
                            "      <td>292.0</td>\n",
                            "      <td>1.539418</td>\n",
                            "      <td>1.089946</td>\n",
                            "      <td>0.05</td>\n",
                            "      <td>0.8000</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>5.50</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>3</th>\n",
                            "      <td>294.0</td>\n",
                            "      <td>1.556327</td>\n",
                            "      <td>1.147365</td>\n",
                            "      <td>0.01</td>\n",
                            "      <td>0.8300</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.8150</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>4</th>\n",
                            "      <td>420.0</td>\n",
                            "      <td>1.249190</td>\n",
                            "      <td>1.034738</td>\n",
                            "      <td>0.05</td>\n",
                            "      <td>0.6000</td>\n",
                            "      <td>1.000</td>\n",
                            "      <td>1.5825</td>\n",
                            "      <td>6.30</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>5</th>\n",
                            "      <td>256.0</td>\n",
                            "      <td>1.428789</td>\n",
                            "      <td>1.144244</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.6200</td>\n",
                            "      <td>1.185</td>\n",
                            "      <td>1.7150</td>\n",
                            "      <td>5.70</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>6</th>\n",
                            "      <td>316.0</td>\n",
                            "      <td>1.313228</td>\n",
                            "      <td>1.065587</td>\n",
                            "      <td>0.09</td>\n",
                            "      <td>0.5600</td>\n",
                            "      <td>1.100</td>\n",
                            "      <td>1.6200</td>\n",
                            "      <td>5.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>7</th>\n",
                            "      <td>316.0</td>\n",
                            "      <td>1.356994</td>\n",
                            "      <td>1.078556</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.6000</td>\n",
                            "      <td>1.120</td>\n",
                            "      <td>1.7425</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>335.0</td>\n",
                            "      <td>1.484925</td>\n",
                            "      <td>1.131495</td>\n",
                            "      <td>0.02</td>\n",
                            "      <td>0.6300</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.9900</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>9</th>\n",
                            "      <td>272.0</td>\n",
                            "      <td>1.614779</td>\n",
                            "      <td>1.164186</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.8075</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>5.09</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>10</th>\n",
                            "      <td>329.0</td>\n",
                            "      <td>1.404742</td>\n",
                            "      <td>1.038701</td>\n",
                            "      <td>0.02</td>\n",
                            "      <td>0.7700</td>\n",
                            "      <td>1.170</td>\n",
                            "      <td>1.7400</td>\n",
                            "      <td>5.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>11</th>\n",
                            "      <td>356.0</td>\n",
                            "      <td>1.390534</td>\n",
                            "      <td>1.159147</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.6775</td>\n",
                            "      <td>1.100</td>\n",
                            "      <td>1.7000</td>\n",
                            "      <td>7.20</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>12</th>\n",
                            "      <td>326.0</td>\n",
                            "      <td>1.533282</td>\n",
                            "      <td>1.158696</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.7400</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>5.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>13</th>\n",
                            "      <td>284.0</td>\n",
                            "      <td>1.421901</td>\n",
                            "      <td>1.080338</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.7000</td>\n",
                            "      <td>1.105</td>\n",
                            "      <td>1.7775</td>\n",
                            "      <td>5.20</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>14</th>\n",
                            "      <td>231.0</td>\n",
                            "      <td>1.692684</td>\n",
                            "      <td>1.372191</td>\n",
                            "      <td>0.05</td>\n",
                            "      <td>0.8200</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>5.90</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>15</th>\n",
                            "      <td>222.0</td>\n",
                            "      <td>1.583964</td>\n",
                            "      <td>1.157553</td>\n",
                            "      <td>0.07</td>\n",
                            "      <td>0.8550</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>1.8400</td>\n",
                            "      <td>5.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>16</th>\n",
                            "      <td>223.0</td>\n",
                            "      <td>1.629910</td>\n",
                            "      <td>1.223131</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.7300</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>2.0000</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>17</th>\n",
                            "      <td>220.0</td>\n",
                            "      <td>1.583682</td>\n",
                            "      <td>1.203617</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.8000</td>\n",
                            "      <td>1.210</td>\n",
                            "      <td>1.9675</td>\n",
                            "      <td>5.20</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>18</th>\n",
                            "      <td>219.0</td>\n",
                            "      <td>1.499772</td>\n",
                            "      <td>1.159497</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.7600</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.8050</td>\n",
                            "      <td>5.90</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>19</th>\n",
                            "      <td>226.0</td>\n",
                            "      <td>1.819469</td>\n",
                            "      <td>1.416291</td>\n",
                            "      <td>0.11</td>\n",
                            "      <td>0.8925</td>\n",
                            "      <td>1.340</td>\n",
                            "      <td>2.1900</td>\n",
                            "      <td>7.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>20</th>\n",
                            "      <td>237.0</td>\n",
                            "      <td>1.553207</td>\n",
                            "      <td>1.296262</td>\n",
                            "      <td>0.02</td>\n",
                            "      <td>0.7000</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>2.0000</td>\n",
                            "      <td>6.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>21</th>\n",
                            "      <td>266.0</td>\n",
                            "      <td>1.332368</td>\n",
                            "      <td>1.032210</td>\n",
                            "      <td>0.03</td>\n",
                            "      <td>0.6050</td>\n",
                            "      <td>1.140</td>\n",
                            "      <td>1.6925</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>22</th>\n",
                            "      <td>215.0</td>\n",
                            "      <td>1.451488</td>\n",
                            "      <td>1.185657</td>\n",
                            "      <td>0.01</td>\n",
                            "      <td>0.7000</td>\n",
                            "      <td>1.180</td>\n",
                            "      <td>1.8000</td>\n",
                            "      <td>5.60</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>23</th>\n",
                            "      <td>233.0</td>\n",
                            "      <td>1.643391</td>\n",
                            "      <td>1.245661</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.8200</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>2.1000</td>\n",
                            "      <td>6.20</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>24</th>\n",
                            "      <td>216.0</td>\n",
                            "      <td>1.553194</td>\n",
                            "      <td>1.144054</td>\n",
                            "      <td>0.03</td>\n",
                            "      <td>0.8375</td>\n",
                            "      <td>1.290</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>6.80</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>25</th>\n",
                            "      <td>238.0</td>\n",
                            "      <td>1.519328</td>\n",
                            "      <td>0.926028</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.8900</td>\n",
                            "      <td>1.400</td>\n",
                            "      <td>1.9950</td>\n",
                            "      <td>5.90</td>\n",
                            "    </tr>\n",
                            "  </tbody>\n",
                            "</table>\n",
                            "</div>"
                        ],
                        "text/plain": [
                            "                count      mean       std   min     25%    50%     75%   max\n",
                            "year month day                                                              \n",
                            "2016 7     27   272.0  1.617574  1.095349  0.06  0.9000  1.400  2.0000  5.60\n",
                            "           28   308.0  1.448149  0.896851  0.10  0.8775  1.240  1.8000  5.10\n",
                            "           29   309.0  1.640129  1.165952  0.01  0.8800  1.450  1.9000  7.70\n",
                            "           30   329.0  1.615076  1.262618  0.03  0.7000  1.240  2.0000  5.70\n",
                            "           31   278.0  1.750827  1.261577  0.10  0.9000  1.500  2.1475  5.90\n",
                            "     8     1    356.0  1.520056  1.157326  0.04  0.8000  1.245  1.8025  6.10\n",
                            "           2    292.0  1.539418  1.089946  0.05  0.8000  1.300  1.9000  5.50\n",
                            "           3    294.0  1.556327  1.147365  0.01  0.8300  1.200  1.8150  5.10\n",
                            "           4    420.0  1.249190  1.034738  0.05  0.6000  1.000  1.5825  6.30\n",
                            "           5    256.0  1.428789  1.144244  0.10  0.6200  1.185  1.7150  5.70\n",
                            "           6    316.0  1.313228  1.065587  0.09  0.5600  1.100  1.6200  5.40\n",
                            "           7    316.0  1.356994  1.078556  0.10  0.6000  1.120  1.7425  5.10\n",
                            "           8    335.0  1.484925  1.131495  0.02  0.6300  1.200  1.9900  5.10\n",
                            "           9    272.0  1.614779  1.164186  0.10  0.8075  1.300  1.9000  5.09\n",
                            "           10   329.0  1.404742  1.038701  0.02  0.7700  1.170  1.7400  5.40\n",
                            "           11   356.0  1.390534  1.159147  0.04  0.6775  1.100  1.7000  7.20\n",
                            "           12   326.0  1.533282  1.158696  0.04  0.7400  1.200  1.9000  5.40\n",
                            "           13   284.0  1.421901  1.080338  0.10  0.7000  1.105  1.7775  5.20\n",
                            "           14   231.0  1.692684  1.372191  0.05  0.8200  1.200  1.9000  5.90\n",
                            "           15   222.0  1.583964  1.157553  0.07  0.8550  1.300  1.8400  5.40\n",
                            "           16   223.0  1.629910  1.223131  0.10  0.7300  1.300  2.0000  5.10\n",
                            "           17   220.0  1.583682  1.203617  0.10  0.8000  1.210  1.9675  5.20\n",
                            "           18   219.0  1.499772  1.159497  0.04  0.7600  1.200  1.8050  5.90\n",
                            "           19   226.0  1.819469  1.416291  0.11  0.8925  1.340  2.1900  7.40\n",
                            "           20   237.0  1.553207  1.296262  0.02  0.7000  1.200  2.0000  6.40\n",
                            "           21   266.0  1.332368  1.032210  0.03  0.6050  1.140  1.6925  5.10\n",
                            "           22   215.0  1.451488  1.185657  0.01  0.7000  1.180  1.8000  5.60\n",
                            "           23   233.0  1.643391  1.245661  0.04  0.8200  1.300  2.1000  6.20\n",
                            "           24   216.0  1.553194  1.144054  0.03  0.8375  1.290  1.9000  6.80\n",
                            "           25   238.0  1.519328  0.926028  0.10  0.8900  1.400  1.9950  5.90"
                        ]
                    },
                    "execution_count": 21,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "df.groupby(['year', 'month', 'day'])['magnitude'].describe()"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "## `apply`\n",
                "\n",
                "Earlier, we saw how arithmetic operators like `+`, `-`, `*`, and `/` apply element-wise to `pandas` `DataFrames` or `Series`.\n"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [],
            "source": [
                "df['magnitude'] * 2"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "What if we wanted to find the length of each value in the name column? You might try something like the following and hope it does an element-wise computation as well."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [],
            "source": [
                "len(df['name'])"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "This is evaluating to the number of elements in the entire `Series`, not the length of each place `name`! Only certain operators support element-wise computation.\n",
                "* Arithmetic operators such as `+`, `-`, `*`, `/`, etc.\n",
                "* Comparison operators such as `==`, `<`, etc.\n",
                "* Logical operators such as `&`, `|`, `~`.\n",
                "\n",
                "Other functions will act on the entire `Series`, just as we saw with `len`!"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Built-in Functions on `pandas`\n",
                "To call the `len` function on each `str`, use the magic syntax below."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [],
            "source": [
                "df['name'].str.len()"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "This reads, \"Take the name column, apply the `len` function defined for `str`s to each element in the `Series`.\" The syntax looks unusual at first, but it helps programmers be clear about the data type and the function to apply to each element! We won't look at other data types now but there is a similar syntax for those as well.\n",
                "\n",
                "Now you aren't limited to just calling `len` here, you can call pretty much any `str` function using this syntax.\n",
                "\n",
                "* `str.lower()` to lower-case each string and return them as a new `Series`.\n",
                "* `str.upper()` to upper-case each string and return them as a new `Series`.\n",
                "* `str.len()` to compute the length of each string and return them as a new `Series`.\n",
                "* `str.strip()`, `str.lstrip()`, `str.rstrip()` to trim whitespace from each string and return them as a new `Series`.\n",
                "\n",
                "For example, the following cell shows how to convert each name to its upper-case version."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [],
            "source": [
                "df['name'].str.upper()"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Note that this operation does not modify the original name column but rather returns a new `Series` with all the names upper-cased.\n",
                "\n",
                "What if you wanted to write your own function to transform a value and apply it to each element in a `Series`? For example, what if I wanted to grab the first two characters from each name? \n",
                "\n",
                "This is where we will need the more general `apply` function defined for `pandas` objects. `apply` is more general than using the specific `str` functions we saw above since it will let you call your own functions on each element. Before we show how to do the specific example of grabbing the first two characters from the names, let's use this new approach to find the `len` of each name."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [],
            "source": [
                "df['name'].apply(len)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "The first part, `df['name'].apply(`, should probably make some sense to you. We are calling some function named `apply` on the `Series` `df['name']`. What's very strange about this is it seems to be passing `len` **as a parameter** to the `apply` function! `len` is not being called directly here but passed as a parameter so that it can be later applied to each element.\n",
                "\n",
                "This is probably the first time that you've seen this syntax. While this does look very strange, this is a feature of Python. A function is, in some sense, just like any other value in Python. But unlike `int`, `str`, or `list`, a Python function doesn't represent data (like numbers, strings, or collections of such data). A Python function represents an algorithm that can later be applied to some data!\n",
                "\n",
                "So the authors of `pandas` who wrote the `apply` function, wrote it to take a parameter that is **another function** like `len`. They then call that function on each element in the `Series`. As Python programmers, we can write our own functions that take other functions as parameters too."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [],
            "source": [
                "def list_apply(values, function):\n",
                "    \"\"\"\n",
                "    Takes a list of values and a function, and applies that function\n",
                "    to each value in values. The given function must take one parameter\n",
                "    as input and the returned list will be the result of calling that\n",
                "    function once for each value in the list.\n",
                "    \"\"\"\n",
                "    # It's not necessary to use a list comprehension here, \n",
                "    # but it's the easiest way to write this method!\n",
                "    return [function(v) for v in values]\n",
                "\n",
                "list_apply(['I', 'love', 'dogs'], len)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "There is no restriction to only passing in the `len` function as a parameter here. You can pass any function that takes a single argument.\n",
                "\n",
                "So if we write a function `first_two` that takes a `str` and returns the first two characters, then we can pass `first_two` to `apply`."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [],
            "source": [
                "def first_two(s):\n",
                "    \"\"\"\n",
                "    Returns the first two characters of the given str as a str.\n",
                "    \n",
                "    Assumes there are at least two characters in s.\n",
                "    \"\"\"\n",
                "    return s[:2]\n",
                "\n",
                "df['name'].apply(first_two)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "**Food for thought:** What happens to the parameter in the function definition? What if we had multiple parameters?"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Saving Results\n",
                "Remember this `apply` function doesn't modify any data in the `DataFrame` or `Series`, but rather returns a new one. It's common that you want to save the result of an `apply` to your dataset to use those values later. Just like how you can use the `[]` assignment syntax for `list` and `dict` types in Python, we can also assign columns directly to a `pandas` `DataFrame`.\n",
                "\n",
                "We can use this syntax to update an existing column."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [],
            "source": [
                "df['name'] = df['name'].str.upper()\n",
                "df"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Or use it to introduce a new column to the `DataFrame`."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [],
            "source": [
                "df['first_two_letters'] = df['name'].apply(first_two)\n",
                "df"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "## Hierarchical indexing\n",
                "\n",
                "Let's revisit `groupby` to take note of something interesting. Take a look at the indices that result from the following `groupby` call:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 28,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/html": [
                            "<div>\n",
                            "<style scoped>\n",
                            "    .dataframe tbody tr th:only-of-type {\n",
                            "        vertical-align: middle;\n",
                            "    }\n",
                            "\n",
                            "    .dataframe tbody tr th {\n",
                            "        vertical-align: top;\n",
                            "    }\n",
                            "\n",
                            "    .dataframe thead th {\n",
                            "        text-align: right;\n",
                            "    }\n",
                            "</style>\n",
                            "<table border=\"1\" class=\"dataframe\">\n",
                            "  <thead>\n",
                            "    <tr style=\"text-align: right;\">\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th>count</th>\n",
                            "      <th>mean</th>\n",
                            "      <th>std</th>\n",
                            "      <th>min</th>\n",
                            "      <th>25%</th>\n",
                            "      <th>50%</th>\n",
                            "      <th>75%</th>\n",
                            "      <th>max</th>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>year</th>\n",
                            "      <th>month</th>\n",
                            "      <th>day</th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "    </tr>\n",
                            "  </thead>\n",
                            "  <tbody>\n",
                            "    <tr>\n",
                            "      <th rowspan=\"30\" valign=\"top\">2016</th>\n",
                            "      <th rowspan=\"5\" valign=\"top\">7</th>\n",
                            "      <th>27</th>\n",
                            "      <td>272.0</td>\n",
                            "      <td>1.617574</td>\n",
                            "      <td>1.095349</td>\n",
                            "      <td>0.06</td>\n",
                            "      <td>0.9000</td>\n",
                            "      <td>1.400</td>\n",
                            "      <td>2.0000</td>\n",
                            "      <td>5.60</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>28</th>\n",
                            "      <td>308.0</td>\n",
                            "      <td>1.448149</td>\n",
                            "      <td>0.896851</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.8775</td>\n",
                            "      <td>1.240</td>\n",
                            "      <td>1.8000</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>29</th>\n",
                            "      <td>309.0</td>\n",
                            "      <td>1.640129</td>\n",
                            "      <td>1.165952</td>\n",
                            "      <td>0.01</td>\n",
                            "      <td>0.8800</td>\n",
                            "      <td>1.450</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>7.70</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>30</th>\n",
                            "      <td>329.0</td>\n",
                            "      <td>1.615076</td>\n",
                            "      <td>1.262618</td>\n",
                            "      <td>0.03</td>\n",
                            "      <td>0.7000</td>\n",
                            "      <td>1.240</td>\n",
                            "      <td>2.0000</td>\n",
                            "      <td>5.70</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>31</th>\n",
                            "      <td>278.0</td>\n",
                            "      <td>1.750827</td>\n",
                            "      <td>1.261577</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.9000</td>\n",
                            "      <td>1.500</td>\n",
                            "      <td>2.1475</td>\n",
                            "      <td>5.90</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th rowspan=\"25\" valign=\"top\">8</th>\n",
                            "      <th>1</th>\n",
                            "      <td>356.0</td>\n",
                            "      <td>1.520056</td>\n",
                            "      <td>1.157326</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.8000</td>\n",
                            "      <td>1.245</td>\n",
                            "      <td>1.8025</td>\n",
                            "      <td>6.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>2</th>\n",
                            "      <td>292.0</td>\n",
                            "      <td>1.539418</td>\n",
                            "      <td>1.089946</td>\n",
                            "      <td>0.05</td>\n",
                            "      <td>0.8000</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>5.50</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>3</th>\n",
                            "      <td>294.0</td>\n",
                            "      <td>1.556327</td>\n",
                            "      <td>1.147365</td>\n",
                            "      <td>0.01</td>\n",
                            "      <td>0.8300</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.8150</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>4</th>\n",
                            "      <td>420.0</td>\n",
                            "      <td>1.249190</td>\n",
                            "      <td>1.034738</td>\n",
                            "      <td>0.05</td>\n",
                            "      <td>0.6000</td>\n",
                            "      <td>1.000</td>\n",
                            "      <td>1.5825</td>\n",
                            "      <td>6.30</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>5</th>\n",
                            "      <td>256.0</td>\n",
                            "      <td>1.428789</td>\n",
                            "      <td>1.144244</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.6200</td>\n",
                            "      <td>1.185</td>\n",
                            "      <td>1.7150</td>\n",
                            "      <td>5.70</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>6</th>\n",
                            "      <td>316.0</td>\n",
                            "      <td>1.313228</td>\n",
                            "      <td>1.065587</td>\n",
                            "      <td>0.09</td>\n",
                            "      <td>0.5600</td>\n",
                            "      <td>1.100</td>\n",
                            "      <td>1.6200</td>\n",
                            "      <td>5.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>7</th>\n",
                            "      <td>316.0</td>\n",
                            "      <td>1.356994</td>\n",
                            "      <td>1.078556</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.6000</td>\n",
                            "      <td>1.120</td>\n",
                            "      <td>1.7425</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>335.0</td>\n",
                            "      <td>1.484925</td>\n",
                            "      <td>1.131495</td>\n",
                            "      <td>0.02</td>\n",
                            "      <td>0.6300</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.9900</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>9</th>\n",
                            "      <td>272.0</td>\n",
                            "      <td>1.614779</td>\n",
                            "      <td>1.164186</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.8075</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>5.09</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>10</th>\n",
                            "      <td>329.0</td>\n",
                            "      <td>1.404742</td>\n",
                            "      <td>1.038701</td>\n",
                            "      <td>0.02</td>\n",
                            "      <td>0.7700</td>\n",
                            "      <td>1.170</td>\n",
                            "      <td>1.7400</td>\n",
                            "      <td>5.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>11</th>\n",
                            "      <td>356.0</td>\n",
                            "      <td>1.390534</td>\n",
                            "      <td>1.159147</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.6775</td>\n",
                            "      <td>1.100</td>\n",
                            "      <td>1.7000</td>\n",
                            "      <td>7.20</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>12</th>\n",
                            "      <td>326.0</td>\n",
                            "      <td>1.533282</td>\n",
                            "      <td>1.158696</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.7400</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>5.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>13</th>\n",
                            "      <td>284.0</td>\n",
                            "      <td>1.421901</td>\n",
                            "      <td>1.080338</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.7000</td>\n",
                            "      <td>1.105</td>\n",
                            "      <td>1.7775</td>\n",
                            "      <td>5.20</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>14</th>\n",
                            "      <td>231.0</td>\n",
                            "      <td>1.692684</td>\n",
                            "      <td>1.372191</td>\n",
                            "      <td>0.05</td>\n",
                            "      <td>0.8200</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>5.90</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>15</th>\n",
                            "      <td>222.0</td>\n",
                            "      <td>1.583964</td>\n",
                            "      <td>1.157553</td>\n",
                            "      <td>0.07</td>\n",
                            "      <td>0.8550</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>1.8400</td>\n",
                            "      <td>5.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>16</th>\n",
                            "      <td>223.0</td>\n",
                            "      <td>1.629910</td>\n",
                            "      <td>1.223131</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.7300</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>2.0000</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>17</th>\n",
                            "      <td>220.0</td>\n",
                            "      <td>1.583682</td>\n",
                            "      <td>1.203617</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.8000</td>\n",
                            "      <td>1.210</td>\n",
                            "      <td>1.9675</td>\n",
                            "      <td>5.20</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>18</th>\n",
                            "      <td>219.0</td>\n",
                            "      <td>1.499772</td>\n",
                            "      <td>1.159497</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.7600</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.8050</td>\n",
                            "      <td>5.90</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>19</th>\n",
                            "      <td>226.0</td>\n",
                            "      <td>1.819469</td>\n",
                            "      <td>1.416291</td>\n",
                            "      <td>0.11</td>\n",
                            "      <td>0.8925</td>\n",
                            "      <td>1.340</td>\n",
                            "      <td>2.1900</td>\n",
                            "      <td>7.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>20</th>\n",
                            "      <td>237.0</td>\n",
                            "      <td>1.553207</td>\n",
                            "      <td>1.296262</td>\n",
                            "      <td>0.02</td>\n",
                            "      <td>0.7000</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>2.0000</td>\n",
                            "      <td>6.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>21</th>\n",
                            "      <td>266.0</td>\n",
                            "      <td>1.332368</td>\n",
                            "      <td>1.032210</td>\n",
                            "      <td>0.03</td>\n",
                            "      <td>0.6050</td>\n",
                            "      <td>1.140</td>\n",
                            "      <td>1.6925</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>22</th>\n",
                            "      <td>215.0</td>\n",
                            "      <td>1.451488</td>\n",
                            "      <td>1.185657</td>\n",
                            "      <td>0.01</td>\n",
                            "      <td>0.7000</td>\n",
                            "      <td>1.180</td>\n",
                            "      <td>1.8000</td>\n",
                            "      <td>5.60</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>23</th>\n",
                            "      <td>233.0</td>\n",
                            "      <td>1.643391</td>\n",
                            "      <td>1.245661</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.8200</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>2.1000</td>\n",
                            "      <td>6.20</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>24</th>\n",
                            "      <td>216.0</td>\n",
                            "      <td>1.553194</td>\n",
                            "      <td>1.144054</td>\n",
                            "      <td>0.03</td>\n",
                            "      <td>0.8375</td>\n",
                            "      <td>1.290</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>6.80</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>25</th>\n",
                            "      <td>238.0</td>\n",
                            "      <td>1.519328</td>\n",
                            "      <td>0.926028</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.8900</td>\n",
                            "      <td>1.400</td>\n",
                            "      <td>1.9950</td>\n",
                            "      <td>5.90</td>\n",
                            "    </tr>\n",
                            "  </tbody>\n",
                            "</table>\n",
                            "</div>"
                        ],
                        "text/plain": [
                            "                count      mean       std   min     25%    50%     75%   max\n",
                            "year month day                                                              \n",
                            "2016 7     27   272.0  1.617574  1.095349  0.06  0.9000  1.400  2.0000  5.60\n",
                            "           28   308.0  1.448149  0.896851  0.10  0.8775  1.240  1.8000  5.10\n",
                            "           29   309.0  1.640129  1.165952  0.01  0.8800  1.450  1.9000  7.70\n",
                            "           30   329.0  1.615076  1.262618  0.03  0.7000  1.240  2.0000  5.70\n",
                            "           31   278.0  1.750827  1.261577  0.10  0.9000  1.500  2.1475  5.90\n",
                            "     8     1    356.0  1.520056  1.157326  0.04  0.8000  1.245  1.8025  6.10\n",
                            "           2    292.0  1.539418  1.089946  0.05  0.8000  1.300  1.9000  5.50\n",
                            "           3    294.0  1.556327  1.147365  0.01  0.8300  1.200  1.8150  5.10\n",
                            "           4    420.0  1.249190  1.034738  0.05  0.6000  1.000  1.5825  6.30\n",
                            "           5    256.0  1.428789  1.144244  0.10  0.6200  1.185  1.7150  5.70\n",
                            "           6    316.0  1.313228  1.065587  0.09  0.5600  1.100  1.6200  5.40\n",
                            "           7    316.0  1.356994  1.078556  0.10  0.6000  1.120  1.7425  5.10\n",
                            "           8    335.0  1.484925  1.131495  0.02  0.6300  1.200  1.9900  5.10\n",
                            "           9    272.0  1.614779  1.164186  0.10  0.8075  1.300  1.9000  5.09\n",
                            "           10   329.0  1.404742  1.038701  0.02  0.7700  1.170  1.7400  5.40\n",
                            "           11   356.0  1.390534  1.159147  0.04  0.6775  1.100  1.7000  7.20\n",
                            "           12   326.0  1.533282  1.158696  0.04  0.7400  1.200  1.9000  5.40\n",
                            "           13   284.0  1.421901  1.080338  0.10  0.7000  1.105  1.7775  5.20\n",
                            "           14   231.0  1.692684  1.372191  0.05  0.8200  1.200  1.9000  5.90\n",
                            "           15   222.0  1.583964  1.157553  0.07  0.8550  1.300  1.8400  5.40\n",
                            "           16   223.0  1.629910  1.223131  0.10  0.7300  1.300  2.0000  5.10\n",
                            "           17   220.0  1.583682  1.203617  0.10  0.8000  1.210  1.9675  5.20\n",
                            "           18   219.0  1.499772  1.159497  0.04  0.7600  1.200  1.8050  5.90\n",
                            "           19   226.0  1.819469  1.416291  0.11  0.8925  1.340  2.1900  7.40\n",
                            "           20   237.0  1.553207  1.296262  0.02  0.7000  1.200  2.0000  6.40\n",
                            "           21   266.0  1.332368  1.032210  0.03  0.6050  1.140  1.6925  5.10\n",
                            "           22   215.0  1.451488  1.185657  0.01  0.7000  1.180  1.8000  5.60\n",
                            "           23   233.0  1.643391  1.245661  0.04  0.8200  1.300  2.1000  6.20\n",
                            "           24   216.0  1.553194  1.144054  0.03  0.8375  1.290  1.9000  6.80\n",
                            "           25   238.0  1.519328  0.926028  0.10  0.8900  1.400  1.9950  5.90"
                        ]
                    },
                    "execution_count": 28,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "magnitudes = df.groupby(['year', 'month', 'day'])['magnitude'].describe()\n",
                "magnitudes"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "In `pandas`, a `DataFrame` can have a **hierarchical index** (or, a multi-level index) called a `MultiIndex`. We can use the `.index` property to investigate this further."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 29,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "MultiIndex([(2016, 7, 27),\n",
                            "            (2016, 7, 28),\n",
                            "            (2016, 7, 29),\n",
                            "            (2016, 7, 30),\n",
                            "            (2016, 7, 31),\n",
                            "            (2016, 8,  1),\n",
                            "            (2016, 8,  2),\n",
                            "            (2016, 8,  3),\n",
                            "            (2016, 8,  4),\n",
                            "            (2016, 8,  5),\n",
                            "            (2016, 8,  6),\n",
                            "            (2016, 8,  7),\n",
                            "            (2016, 8,  8),\n",
                            "            (2016, 8,  9),\n",
                            "            (2016, 8, 10),\n",
                            "            (2016, 8, 11),\n",
                            "            (2016, 8, 12),\n",
                            "            (2016, 8, 13),\n",
                            "            (2016, 8, 14),\n",
                            "            (2016, 8, 15),\n",
                            "            (2016, 8, 16),\n",
                            "            (2016, 8, 17),\n",
                            "            (2016, 8, 18),\n",
                            "            (2016, 8, 19),\n",
                            "            (2016, 8, 20),\n",
                            "            (2016, 8, 21),\n",
                            "            (2016, 8, 22),\n",
                            "            (2016, 8, 23),\n",
                            "            (2016, 8, 24),\n",
                            "            (2016, 8, 25)],\n",
                            "           names=['year', 'month', 'day'])"
                        ]
                    },
                    "execution_count": 29,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "magnitudes.index"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "**Food for thought:** See a familiar data structure?\n",
                "\n",
                "The `MultiIndex` comes in handy when your data might have multiple categorical dimensions. It allows us to work with and manipulate data with multiple levels as though it were one. Some common use cases are:\n",
                "\n",
                "* Time-series data with multiple columns for time units (like the year, month, and day in `earthquakes.csv`)\n",
                "* Experimental data with multiple factors that are difficult to represent in two dimensions\n",
                "* Geographical data with nested location columns (such as country, state, city)\n",
                "* Grouping data on multiple dimensions (hence why we see it with multi-column `groupby`!)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Indexing a `MultiIndex`\n",
                "\n",
                "We can use `.loc` with `MultiIndex`, but the syntax will look a bit strange. Recall that `.loc[]` takes in a row indexer and a column indexer, like so:\n",
                "\n",
                "```python\n",
                "df.loc[row_indexer, column_indexer]\n",
                "```\n",
                "\n",
                "To select a specific combination of values in the `MultiIndex`, you would need to use a `tuple`."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 31,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "count    316.000000\n",
                            "mean       1.356994\n",
                            "std        1.078556\n",
                            "min        0.100000\n",
                            "25%        0.600000\n",
                            "50%        1.120000\n",
                            "75%        1.742500\n",
                            "max        5.100000\n",
                            "Name: (2016, 8, 7), dtype: float64"
                        ]
                    },
                    "execution_count": 31,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "magnitudes.loc[(2016, 8, 7), :]"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Even though there are three values in the `MultiIndex`, we don't need to select all of them! In the following slice, we have:\n",
                "\n",
                "* The `'year'` index set to `2016`\n",
                "* The `'month'` index set to `8`\n",
                "\n",
                "Notice that we didn't specify a `'day'` index, so we still see all the possible `'day'` values that have a `'year'` of `2016` and a `'month'` of `8`."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 32,
            "metadata": {},
            "outputs": [
                {
                    "data": {
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                            "<table border=\"1\" class=\"dataframe\">\n",
                            "  <thead>\n",
                            "    <tr style=\"text-align: right;\">\n",
                            "      <th></th>\n",
                            "      <th>count</th>\n",
                            "      <th>mean</th>\n",
                            "      <th>std</th>\n",
                            "      <th>min</th>\n",
                            "      <th>25%</th>\n",
                            "      <th>50%</th>\n",
                            "      <th>75%</th>\n",
                            "      <th>max</th>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>day</th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "    </tr>\n",
                            "  </thead>\n",
                            "  <tbody>\n",
                            "    <tr>\n",
                            "      <th>1</th>\n",
                            "      <td>356.0</td>\n",
                            "      <td>1.520056</td>\n",
                            "      <td>1.157326</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.8000</td>\n",
                            "      <td>1.245</td>\n",
                            "      <td>1.8025</td>\n",
                            "      <td>6.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>2</th>\n",
                            "      <td>292.0</td>\n",
                            "      <td>1.539418</td>\n",
                            "      <td>1.089946</td>\n",
                            "      <td>0.05</td>\n",
                            "      <td>0.8000</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>5.50</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>3</th>\n",
                            "      <td>294.0</td>\n",
                            "      <td>1.556327</td>\n",
                            "      <td>1.147365</td>\n",
                            "      <td>0.01</td>\n",
                            "      <td>0.8300</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.8150</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>4</th>\n",
                            "      <td>420.0</td>\n",
                            "      <td>1.249190</td>\n",
                            "      <td>1.034738</td>\n",
                            "      <td>0.05</td>\n",
                            "      <td>0.6000</td>\n",
                            "      <td>1.000</td>\n",
                            "      <td>1.5825</td>\n",
                            "      <td>6.30</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>5</th>\n",
                            "      <td>256.0</td>\n",
                            "      <td>1.428789</td>\n",
                            "      <td>1.144244</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.6200</td>\n",
                            "      <td>1.185</td>\n",
                            "      <td>1.7150</td>\n",
                            "      <td>5.70</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>6</th>\n",
                            "      <td>316.0</td>\n",
                            "      <td>1.313228</td>\n",
                            "      <td>1.065587</td>\n",
                            "      <td>0.09</td>\n",
                            "      <td>0.5600</td>\n",
                            "      <td>1.100</td>\n",
                            "      <td>1.6200</td>\n",
                            "      <td>5.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>7</th>\n",
                            "      <td>316.0</td>\n",
                            "      <td>1.356994</td>\n",
                            "      <td>1.078556</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.6000</td>\n",
                            "      <td>1.120</td>\n",
                            "      <td>1.7425</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>335.0</td>\n",
                            "      <td>1.484925</td>\n",
                            "      <td>1.131495</td>\n",
                            "      <td>0.02</td>\n",
                            "      <td>0.6300</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.9900</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>9</th>\n",
                            "      <td>272.0</td>\n",
                            "      <td>1.614779</td>\n",
                            "      <td>1.164186</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.8075</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>5.09</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>10</th>\n",
                            "      <td>329.0</td>\n",
                            "      <td>1.404742</td>\n",
                            "      <td>1.038701</td>\n",
                            "      <td>0.02</td>\n",
                            "      <td>0.7700</td>\n",
                            "      <td>1.170</td>\n",
                            "      <td>1.7400</td>\n",
                            "      <td>5.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>11</th>\n",
                            "      <td>356.0</td>\n",
                            "      <td>1.390534</td>\n",
                            "      <td>1.159147</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.6775</td>\n",
                            "      <td>1.100</td>\n",
                            "      <td>1.7000</td>\n",
                            "      <td>7.20</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>12</th>\n",
                            "      <td>326.0</td>\n",
                            "      <td>1.533282</td>\n",
                            "      <td>1.158696</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.7400</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>5.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>13</th>\n",
                            "      <td>284.0</td>\n",
                            "      <td>1.421901</td>\n",
                            "      <td>1.080338</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.7000</td>\n",
                            "      <td>1.105</td>\n",
                            "      <td>1.7775</td>\n",
                            "      <td>5.20</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>14</th>\n",
                            "      <td>231.0</td>\n",
                            "      <td>1.692684</td>\n",
                            "      <td>1.372191</td>\n",
                            "      <td>0.05</td>\n",
                            "      <td>0.8200</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>5.90</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>15</th>\n",
                            "      <td>222.0</td>\n",
                            "      <td>1.583964</td>\n",
                            "      <td>1.157553</td>\n",
                            "      <td>0.07</td>\n",
                            "      <td>0.8550</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>1.8400</td>\n",
                            "      <td>5.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>16</th>\n",
                            "      <td>223.0</td>\n",
                            "      <td>1.629910</td>\n",
                            "      <td>1.223131</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.7300</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>2.0000</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>17</th>\n",
                            "      <td>220.0</td>\n",
                            "      <td>1.583682</td>\n",
                            "      <td>1.203617</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.8000</td>\n",
                            "      <td>1.210</td>\n",
                            "      <td>1.9675</td>\n",
                            "      <td>5.20</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>18</th>\n",
                            "      <td>219.0</td>\n",
                            "      <td>1.499772</td>\n",
                            "      <td>1.159497</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.7600</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.8050</td>\n",
                            "      <td>5.90</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>19</th>\n",
                            "      <td>226.0</td>\n",
                            "      <td>1.819469</td>\n",
                            "      <td>1.416291</td>\n",
                            "      <td>0.11</td>\n",
                            "      <td>0.8925</td>\n",
                            "      <td>1.340</td>\n",
                            "      <td>2.1900</td>\n",
                            "      <td>7.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>20</th>\n",
                            "      <td>237.0</td>\n",
                            "      <td>1.553207</td>\n",
                            "      <td>1.296262</td>\n",
                            "      <td>0.02</td>\n",
                            "      <td>0.7000</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>2.0000</td>\n",
                            "      <td>6.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>21</th>\n",
                            "      <td>266.0</td>\n",
                            "      <td>1.332368</td>\n",
                            "      <td>1.032210</td>\n",
                            "      <td>0.03</td>\n",
                            "      <td>0.6050</td>\n",
                            "      <td>1.140</td>\n",
                            "      <td>1.6925</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>22</th>\n",
                            "      <td>215.0</td>\n",
                            "      <td>1.451488</td>\n",
                            "      <td>1.185657</td>\n",
                            "      <td>0.01</td>\n",
                            "      <td>0.7000</td>\n",
                            "      <td>1.180</td>\n",
                            "      <td>1.8000</td>\n",
                            "      <td>5.60</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>23</th>\n",
                            "      <td>233.0</td>\n",
                            "      <td>1.643391</td>\n",
                            "      <td>1.245661</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.8200</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>2.1000</td>\n",
                            "      <td>6.20</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>24</th>\n",
                            "      <td>216.0</td>\n",
                            "      <td>1.553194</td>\n",
                            "      <td>1.144054</td>\n",
                            "      <td>0.03</td>\n",
                            "      <td>0.8375</td>\n",
                            "      <td>1.290</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>6.80</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>25</th>\n",
                            "      <td>238.0</td>\n",
                            "      <td>1.519328</td>\n",
                            "      <td>0.926028</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.8900</td>\n",
                            "      <td>1.400</td>\n",
                            "      <td>1.9950</td>\n",
                            "      <td>5.90</td>\n",
                            "    </tr>\n",
                            "  </tbody>\n",
                            "</table>\n",
                            "</div>"
                        ],
                        "text/plain": [
                            "     count      mean       std   min     25%    50%     75%   max\n",
                            "day                                                              \n",
                            "1    356.0  1.520056  1.157326  0.04  0.8000  1.245  1.8025  6.10\n",
                            "2    292.0  1.539418  1.089946  0.05  0.8000  1.300  1.9000  5.50\n",
                            "3    294.0  1.556327  1.147365  0.01  0.8300  1.200  1.8150  5.10\n",
                            "4    420.0  1.249190  1.034738  0.05  0.6000  1.000  1.5825  6.30\n",
                            "5    256.0  1.428789  1.144244  0.10  0.6200  1.185  1.7150  5.70\n",
                            "6    316.0  1.313228  1.065587  0.09  0.5600  1.100  1.6200  5.40\n",
                            "7    316.0  1.356994  1.078556  0.10  0.6000  1.120  1.7425  5.10\n",
                            "8    335.0  1.484925  1.131495  0.02  0.6300  1.200  1.9900  5.10\n",
                            "9    272.0  1.614779  1.164186  0.10  0.8075  1.300  1.9000  5.09\n",
                            "10   329.0  1.404742  1.038701  0.02  0.7700  1.170  1.7400  5.40\n",
                            "11   356.0  1.390534  1.159147  0.04  0.6775  1.100  1.7000  7.20\n",
                            "12   326.0  1.533282  1.158696  0.04  0.7400  1.200  1.9000  5.40\n",
                            "13   284.0  1.421901  1.080338  0.10  0.7000  1.105  1.7775  5.20\n",
                            "14   231.0  1.692684  1.372191  0.05  0.8200  1.200  1.9000  5.90\n",
                            "15   222.0  1.583964  1.157553  0.07  0.8550  1.300  1.8400  5.40\n",
                            "16   223.0  1.629910  1.223131  0.10  0.7300  1.300  2.0000  5.10\n",
                            "17   220.0  1.583682  1.203617  0.10  0.8000  1.210  1.9675  5.20\n",
                            "18   219.0  1.499772  1.159497  0.04  0.7600  1.200  1.8050  5.90\n",
                            "19   226.0  1.819469  1.416291  0.11  0.8925  1.340  2.1900  7.40\n",
                            "20   237.0  1.553207  1.296262  0.02  0.7000  1.200  2.0000  6.40\n",
                            "21   266.0  1.332368  1.032210  0.03  0.6050  1.140  1.6925  5.10\n",
                            "22   215.0  1.451488  1.185657  0.01  0.7000  1.180  1.8000  5.60\n",
                            "23   233.0  1.643391  1.245661  0.04  0.8200  1.300  2.1000  6.20\n",
                            "24   216.0  1.553194  1.144054  0.03  0.8375  1.290  1.9000  6.80\n",
                            "25   238.0  1.519328  0.926028  0.10  0.8900  1.400  1.9950  5.90"
                        ]
                    },
                    "execution_count": 32,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "magnitudes.loc[(2016, 8), :]"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "We can use `slice(None)` to select all values at a particular level. So, if we wanted all the values in August (when `'month'` is `8`) and it didn't matter what day or year it was, we might do the following:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 45,
            "metadata": {},
            "outputs": [
                {
                    "data": {
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                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th>count</th>\n",
                            "      <th>mean</th>\n",
                            "      <th>std</th>\n",
                            "      <th>min</th>\n",
                            "      <th>25%</th>\n",
                            "      <th>50%</th>\n",
                            "      <th>75%</th>\n",
                            "      <th>max</th>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>year</th>\n",
                            "      <th>month</th>\n",
                            "      <th>day</th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "    </tr>\n",
                            "  </thead>\n",
                            "  <tbody>\n",
                            "    <tr>\n",
                            "      <th rowspan=\"25\" valign=\"top\">2016</th>\n",
                            "      <th rowspan=\"25\" valign=\"top\">8</th>\n",
                            "      <th>1</th>\n",
                            "      <td>356.0</td>\n",
                            "      <td>1.520056</td>\n",
                            "      <td>1.157326</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.8000</td>\n",
                            "      <td>1.245</td>\n",
                            "      <td>1.8025</td>\n",
                            "      <td>6.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>2</th>\n",
                            "      <td>292.0</td>\n",
                            "      <td>1.539418</td>\n",
                            "      <td>1.089946</td>\n",
                            "      <td>0.05</td>\n",
                            "      <td>0.8000</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>5.50</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>3</th>\n",
                            "      <td>294.0</td>\n",
                            "      <td>1.556327</td>\n",
                            "      <td>1.147365</td>\n",
                            "      <td>0.01</td>\n",
                            "      <td>0.8300</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.8150</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>4</th>\n",
                            "      <td>420.0</td>\n",
                            "      <td>1.249190</td>\n",
                            "      <td>1.034738</td>\n",
                            "      <td>0.05</td>\n",
                            "      <td>0.6000</td>\n",
                            "      <td>1.000</td>\n",
                            "      <td>1.5825</td>\n",
                            "      <td>6.30</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>5</th>\n",
                            "      <td>256.0</td>\n",
                            "      <td>1.428789</td>\n",
                            "      <td>1.144244</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.6200</td>\n",
                            "      <td>1.185</td>\n",
                            "      <td>1.7150</td>\n",
                            "      <td>5.70</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>6</th>\n",
                            "      <td>316.0</td>\n",
                            "      <td>1.313228</td>\n",
                            "      <td>1.065587</td>\n",
                            "      <td>0.09</td>\n",
                            "      <td>0.5600</td>\n",
                            "      <td>1.100</td>\n",
                            "      <td>1.6200</td>\n",
                            "      <td>5.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>7</th>\n",
                            "      <td>316.0</td>\n",
                            "      <td>1.356994</td>\n",
                            "      <td>1.078556</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.6000</td>\n",
                            "      <td>1.120</td>\n",
                            "      <td>1.7425</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>335.0</td>\n",
                            "      <td>1.484925</td>\n",
                            "      <td>1.131495</td>\n",
                            "      <td>0.02</td>\n",
                            "      <td>0.6300</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.9900</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>9</th>\n",
                            "      <td>272.0</td>\n",
                            "      <td>1.614779</td>\n",
                            "      <td>1.164186</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.8075</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>5.09</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>10</th>\n",
                            "      <td>329.0</td>\n",
                            "      <td>1.404742</td>\n",
                            "      <td>1.038701</td>\n",
                            "      <td>0.02</td>\n",
                            "      <td>0.7700</td>\n",
                            "      <td>1.170</td>\n",
                            "      <td>1.7400</td>\n",
                            "      <td>5.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>11</th>\n",
                            "      <td>356.0</td>\n",
                            "      <td>1.390534</td>\n",
                            "      <td>1.159147</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.6775</td>\n",
                            "      <td>1.100</td>\n",
                            "      <td>1.7000</td>\n",
                            "      <td>7.20</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>12</th>\n",
                            "      <td>326.0</td>\n",
                            "      <td>1.533282</td>\n",
                            "      <td>1.158696</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.7400</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>5.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>13</th>\n",
                            "      <td>284.0</td>\n",
                            "      <td>1.421901</td>\n",
                            "      <td>1.080338</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.7000</td>\n",
                            "      <td>1.105</td>\n",
                            "      <td>1.7775</td>\n",
                            "      <td>5.20</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>14</th>\n",
                            "      <td>231.0</td>\n",
                            "      <td>1.692684</td>\n",
                            "      <td>1.372191</td>\n",
                            "      <td>0.05</td>\n",
                            "      <td>0.8200</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>5.90</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>15</th>\n",
                            "      <td>222.0</td>\n",
                            "      <td>1.583964</td>\n",
                            "      <td>1.157553</td>\n",
                            "      <td>0.07</td>\n",
                            "      <td>0.8550</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>1.8400</td>\n",
                            "      <td>5.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>16</th>\n",
                            "      <td>223.0</td>\n",
                            "      <td>1.629910</td>\n",
                            "      <td>1.223131</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.7300</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>2.0000</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>17</th>\n",
                            "      <td>220.0</td>\n",
                            "      <td>1.583682</td>\n",
                            "      <td>1.203617</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.8000</td>\n",
                            "      <td>1.210</td>\n",
                            "      <td>1.9675</td>\n",
                            "      <td>5.20</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>18</th>\n",
                            "      <td>219.0</td>\n",
                            "      <td>1.499772</td>\n",
                            "      <td>1.159497</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.7600</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.8050</td>\n",
                            "      <td>5.90</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>19</th>\n",
                            "      <td>226.0</td>\n",
                            "      <td>1.819469</td>\n",
                            "      <td>1.416291</td>\n",
                            "      <td>0.11</td>\n",
                            "      <td>0.8925</td>\n",
                            "      <td>1.340</td>\n",
                            "      <td>2.1900</td>\n",
                            "      <td>7.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>20</th>\n",
                            "      <td>237.0</td>\n",
                            "      <td>1.553207</td>\n",
                            "      <td>1.296262</td>\n",
                            "      <td>0.02</td>\n",
                            "      <td>0.7000</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>2.0000</td>\n",
                            "      <td>6.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>21</th>\n",
                            "      <td>266.0</td>\n",
                            "      <td>1.332368</td>\n",
                            "      <td>1.032210</td>\n",
                            "      <td>0.03</td>\n",
                            "      <td>0.6050</td>\n",
                            "      <td>1.140</td>\n",
                            "      <td>1.6925</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>22</th>\n",
                            "      <td>215.0</td>\n",
                            "      <td>1.451488</td>\n",
                            "      <td>1.185657</td>\n",
                            "      <td>0.01</td>\n",
                            "      <td>0.7000</td>\n",
                            "      <td>1.180</td>\n",
                            "      <td>1.8000</td>\n",
                            "      <td>5.60</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>23</th>\n",
                            "      <td>233.0</td>\n",
                            "      <td>1.643391</td>\n",
                            "      <td>1.245661</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.8200</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>2.1000</td>\n",
                            "      <td>6.20</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>24</th>\n",
                            "      <td>216.0</td>\n",
                            "      <td>1.553194</td>\n",
                            "      <td>1.144054</td>\n",
                            "      <td>0.03</td>\n",
                            "      <td>0.8375</td>\n",
                            "      <td>1.290</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>6.80</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>25</th>\n",
                            "      <td>238.0</td>\n",
                            "      <td>1.519328</td>\n",
                            "      <td>0.926028</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.8900</td>\n",
                            "      <td>1.400</td>\n",
                            "      <td>1.9950</td>\n",
                            "      <td>5.90</td>\n",
                            "    </tr>\n",
                            "  </tbody>\n",
                            "</table>\n",
                            "</div>"
                        ],
                        "text/plain": [
                            "                count      mean       std   min     25%    50%     75%   max\n",
                            "year month day                                                              \n",
                            "2016 8     1    356.0  1.520056  1.157326  0.04  0.8000  1.245  1.8025  6.10\n",
                            "           2    292.0  1.539418  1.089946  0.05  0.8000  1.300  1.9000  5.50\n",
                            "           3    294.0  1.556327  1.147365  0.01  0.8300  1.200  1.8150  5.10\n",
                            "           4    420.0  1.249190  1.034738  0.05  0.6000  1.000  1.5825  6.30\n",
                            "           5    256.0  1.428789  1.144244  0.10  0.6200  1.185  1.7150  5.70\n",
                            "           6    316.0  1.313228  1.065587  0.09  0.5600  1.100  1.6200  5.40\n",
                            "           7    316.0  1.356994  1.078556  0.10  0.6000  1.120  1.7425  5.10\n",
                            "           8    335.0  1.484925  1.131495  0.02  0.6300  1.200  1.9900  5.10\n",
                            "           9    272.0  1.614779  1.164186  0.10  0.8075  1.300  1.9000  5.09\n",
                            "           10   329.0  1.404742  1.038701  0.02  0.7700  1.170  1.7400  5.40\n",
                            "           11   356.0  1.390534  1.159147  0.04  0.6775  1.100  1.7000  7.20\n",
                            "           12   326.0  1.533282  1.158696  0.04  0.7400  1.200  1.9000  5.40\n",
                            "           13   284.0  1.421901  1.080338  0.10  0.7000  1.105  1.7775  5.20\n",
                            "           14   231.0  1.692684  1.372191  0.05  0.8200  1.200  1.9000  5.90\n",
                            "           15   222.0  1.583964  1.157553  0.07  0.8550  1.300  1.8400  5.40\n",
                            "           16   223.0  1.629910  1.223131  0.10  0.7300  1.300  2.0000  5.10\n",
                            "           17   220.0  1.583682  1.203617  0.10  0.8000  1.210  1.9675  5.20\n",
                            "           18   219.0  1.499772  1.159497  0.04  0.7600  1.200  1.8050  5.90\n",
                            "           19   226.0  1.819469  1.416291  0.11  0.8925  1.340  2.1900  7.40\n",
                            "           20   237.0  1.553207  1.296262  0.02  0.7000  1.200  2.0000  6.40\n",
                            "           21   266.0  1.332368  1.032210  0.03  0.6050  1.140  1.6925  5.10\n",
                            "           22   215.0  1.451488  1.185657  0.01  0.7000  1.180  1.8000  5.60\n",
                            "           23   233.0  1.643391  1.245661  0.04  0.8200  1.300  2.1000  6.20\n",
                            "           24   216.0  1.553194  1.144054  0.03  0.8375  1.290  1.9000  6.80\n",
                            "           25   238.0  1.519328  0.926028  0.10  0.8900  1.400  1.9950  5.90"
                        ]
                    },
                    "execution_count": 45,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "magnitudes.loc[(slice(None), 8, slice(None)), :]"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Resetting Indices\n",
                "\n",
                "The `.reset_index()` method converts index levels back into regular columns. This is useful when you need to perform column-wise operations or when you want to \"flatten\" your data structure.\n",
                "\n",
                "By default, `.reset_index()` moves all index levels to their own columns and assigns integer indices starting from 0:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 46,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/html": [
                            "<div>\n",
                            "<style scoped>\n",
                            "    .dataframe tbody tr th:only-of-type {\n",
                            "        vertical-align: middle;\n",
                            "    }\n",
                            "\n",
                            "    .dataframe tbody tr th {\n",
                            "        vertical-align: top;\n",
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                            "\n",
                            "    .dataframe thead th {\n",
                            "        text-align: right;\n",
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                            "</style>\n",
                            "<table border=\"1\" class=\"dataframe\">\n",
                            "  <thead>\n",
                            "    <tr style=\"text-align: right;\">\n",
                            "      <th></th>\n",
                            "      <th>year</th>\n",
                            "      <th>month</th>\n",
                            "      <th>day</th>\n",
                            "      <th>count</th>\n",
                            "      <th>mean</th>\n",
                            "      <th>std</th>\n",
                            "      <th>min</th>\n",
                            "      <th>25%</th>\n",
                            "      <th>50%</th>\n",
                            "      <th>75%</th>\n",
                            "      <th>max</th>\n",
                            "    </tr>\n",
                            "  </thead>\n",
                            "  <tbody>\n",
                            "    <tr>\n",
                            "      <th>0</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>7</td>\n",
                            "      <td>27</td>\n",
                            "      <td>272.0</td>\n",
                            "      <td>1.617574</td>\n",
                            "      <td>1.095349</td>\n",
                            "      <td>0.06</td>\n",
                            "      <td>0.9000</td>\n",
                            "      <td>1.400</td>\n",
                            "      <td>2.0000</td>\n",
                            "      <td>5.60</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>1</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>7</td>\n",
                            "      <td>28</td>\n",
                            "      <td>308.0</td>\n",
                            "      <td>1.448149</td>\n",
                            "      <td>0.896851</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.8775</td>\n",
                            "      <td>1.240</td>\n",
                            "      <td>1.8000</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>2</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>7</td>\n",
                            "      <td>29</td>\n",
                            "      <td>309.0</td>\n",
                            "      <td>1.640129</td>\n",
                            "      <td>1.165952</td>\n",
                            "      <td>0.01</td>\n",
                            "      <td>0.8800</td>\n",
                            "      <td>1.450</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>7.70</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>3</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>7</td>\n",
                            "      <td>30</td>\n",
                            "      <td>329.0</td>\n",
                            "      <td>1.615076</td>\n",
                            "      <td>1.262618</td>\n",
                            "      <td>0.03</td>\n",
                            "      <td>0.7000</td>\n",
                            "      <td>1.240</td>\n",
                            "      <td>2.0000</td>\n",
                            "      <td>5.70</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>4</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>7</td>\n",
                            "      <td>31</td>\n",
                            "      <td>278.0</td>\n",
                            "      <td>1.750827</td>\n",
                            "      <td>1.261577</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.9000</td>\n",
                            "      <td>1.500</td>\n",
                            "      <td>2.1475</td>\n",
                            "      <td>5.90</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>5</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>1</td>\n",
                            "      <td>356.0</td>\n",
                            "      <td>1.520056</td>\n",
                            "      <td>1.157326</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.8000</td>\n",
                            "      <td>1.245</td>\n",
                            "      <td>1.8025</td>\n",
                            "      <td>6.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>6</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>2</td>\n",
                            "      <td>292.0</td>\n",
                            "      <td>1.539418</td>\n",
                            "      <td>1.089946</td>\n",
                            "      <td>0.05</td>\n",
                            "      <td>0.8000</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>5.50</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>7</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>3</td>\n",
                            "      <td>294.0</td>\n",
                            "      <td>1.556327</td>\n",
                            "      <td>1.147365</td>\n",
                            "      <td>0.01</td>\n",
                            "      <td>0.8300</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.8150</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>4</td>\n",
                            "      <td>420.0</td>\n",
                            "      <td>1.249190</td>\n",
                            "      <td>1.034738</td>\n",
                            "      <td>0.05</td>\n",
                            "      <td>0.6000</td>\n",
                            "      <td>1.000</td>\n",
                            "      <td>1.5825</td>\n",
                            "      <td>6.30</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>9</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>5</td>\n",
                            "      <td>256.0</td>\n",
                            "      <td>1.428789</td>\n",
                            "      <td>1.144244</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.6200</td>\n",
                            "      <td>1.185</td>\n",
                            "      <td>1.7150</td>\n",
                            "      <td>5.70</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>10</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>6</td>\n",
                            "      <td>316.0</td>\n",
                            "      <td>1.313228</td>\n",
                            "      <td>1.065587</td>\n",
                            "      <td>0.09</td>\n",
                            "      <td>0.5600</td>\n",
                            "      <td>1.100</td>\n",
                            "      <td>1.6200</td>\n",
                            "      <td>5.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>11</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>7</td>\n",
                            "      <td>316.0</td>\n",
                            "      <td>1.356994</td>\n",
                            "      <td>1.078556</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.6000</td>\n",
                            "      <td>1.120</td>\n",
                            "      <td>1.7425</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>12</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>8</td>\n",
                            "      <td>335.0</td>\n",
                            "      <td>1.484925</td>\n",
                            "      <td>1.131495</td>\n",
                            "      <td>0.02</td>\n",
                            "      <td>0.6300</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.9900</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>13</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>9</td>\n",
                            "      <td>272.0</td>\n",
                            "      <td>1.614779</td>\n",
                            "      <td>1.164186</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.8075</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>5.09</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>14</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>10</td>\n",
                            "      <td>329.0</td>\n",
                            "      <td>1.404742</td>\n",
                            "      <td>1.038701</td>\n",
                            "      <td>0.02</td>\n",
                            "      <td>0.7700</td>\n",
                            "      <td>1.170</td>\n",
                            "      <td>1.7400</td>\n",
                            "      <td>5.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>15</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>11</td>\n",
                            "      <td>356.0</td>\n",
                            "      <td>1.390534</td>\n",
                            "      <td>1.159147</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.6775</td>\n",
                            "      <td>1.100</td>\n",
                            "      <td>1.7000</td>\n",
                            "      <td>7.20</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>16</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>12</td>\n",
                            "      <td>326.0</td>\n",
                            "      <td>1.533282</td>\n",
                            "      <td>1.158696</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.7400</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>5.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>17</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>13</td>\n",
                            "      <td>284.0</td>\n",
                            "      <td>1.421901</td>\n",
                            "      <td>1.080338</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.7000</td>\n",
                            "      <td>1.105</td>\n",
                            "      <td>1.7775</td>\n",
                            "      <td>5.20</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>18</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>14</td>\n",
                            "      <td>231.0</td>\n",
                            "      <td>1.692684</td>\n",
                            "      <td>1.372191</td>\n",
                            "      <td>0.05</td>\n",
                            "      <td>0.8200</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>5.90</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>19</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>15</td>\n",
                            "      <td>222.0</td>\n",
                            "      <td>1.583964</td>\n",
                            "      <td>1.157553</td>\n",
                            "      <td>0.07</td>\n",
                            "      <td>0.8550</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>1.8400</td>\n",
                            "      <td>5.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>20</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>16</td>\n",
                            "      <td>223.0</td>\n",
                            "      <td>1.629910</td>\n",
                            "      <td>1.223131</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.7300</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>2.0000</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>21</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>17</td>\n",
                            "      <td>220.0</td>\n",
                            "      <td>1.583682</td>\n",
                            "      <td>1.203617</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.8000</td>\n",
                            "      <td>1.210</td>\n",
                            "      <td>1.9675</td>\n",
                            "      <td>5.20</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>22</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>18</td>\n",
                            "      <td>219.0</td>\n",
                            "      <td>1.499772</td>\n",
                            "      <td>1.159497</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.7600</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.8050</td>\n",
                            "      <td>5.90</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>23</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>19</td>\n",
                            "      <td>226.0</td>\n",
                            "      <td>1.819469</td>\n",
                            "      <td>1.416291</td>\n",
                            "      <td>0.11</td>\n",
                            "      <td>0.8925</td>\n",
                            "      <td>1.340</td>\n",
                            "      <td>2.1900</td>\n",
                            "      <td>7.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>24</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>20</td>\n",
                            "      <td>237.0</td>\n",
                            "      <td>1.553207</td>\n",
                            "      <td>1.296262</td>\n",
                            "      <td>0.02</td>\n",
                            "      <td>0.7000</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>2.0000</td>\n",
                            "      <td>6.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>25</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>21</td>\n",
                            "      <td>266.0</td>\n",
                            "      <td>1.332368</td>\n",
                            "      <td>1.032210</td>\n",
                            "      <td>0.03</td>\n",
                            "      <td>0.6050</td>\n",
                            "      <td>1.140</td>\n",
                            "      <td>1.6925</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>26</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>22</td>\n",
                            "      <td>215.0</td>\n",
                            "      <td>1.451488</td>\n",
                            "      <td>1.185657</td>\n",
                            "      <td>0.01</td>\n",
                            "      <td>0.7000</td>\n",
                            "      <td>1.180</td>\n",
                            "      <td>1.8000</td>\n",
                            "      <td>5.60</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>27</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>23</td>\n",
                            "      <td>233.0</td>\n",
                            "      <td>1.643391</td>\n",
                            "      <td>1.245661</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.8200</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>2.1000</td>\n",
                            "      <td>6.20</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>28</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>24</td>\n",
                            "      <td>216.0</td>\n",
                            "      <td>1.553194</td>\n",
                            "      <td>1.144054</td>\n",
                            "      <td>0.03</td>\n",
                            "      <td>0.8375</td>\n",
                            "      <td>1.290</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>6.80</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>29</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>25</td>\n",
                            "      <td>238.0</td>\n",
                            "      <td>1.519328</td>\n",
                            "      <td>0.926028</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.8900</td>\n",
                            "      <td>1.400</td>\n",
                            "      <td>1.9950</td>\n",
                            "      <td>5.90</td>\n",
                            "    </tr>\n",
                            "  </tbody>\n",
                            "</table>\n",
                            "</div>"
                        ],
                        "text/plain": [
                            "    year  month  day  count      mean       std   min     25%    50%     75%  \\\n",
                            "0   2016      7   27  272.0  1.617574  1.095349  0.06  0.9000  1.400  2.0000   \n",
                            "1   2016      7   28  308.0  1.448149  0.896851  0.10  0.8775  1.240  1.8000   \n",
                            "2   2016      7   29  309.0  1.640129  1.165952  0.01  0.8800  1.450  1.9000   \n",
                            "3   2016      7   30  329.0  1.615076  1.262618  0.03  0.7000  1.240  2.0000   \n",
                            "4   2016      7   31  278.0  1.750827  1.261577  0.10  0.9000  1.500  2.1475   \n",
                            "5   2016      8    1  356.0  1.520056  1.157326  0.04  0.8000  1.245  1.8025   \n",
                            "6   2016      8    2  292.0  1.539418  1.089946  0.05  0.8000  1.300  1.9000   \n",
                            "7   2016      8    3  294.0  1.556327  1.147365  0.01  0.8300  1.200  1.8150   \n",
                            "8   2016      8    4  420.0  1.249190  1.034738  0.05  0.6000  1.000  1.5825   \n",
                            "9   2016      8    5  256.0  1.428789  1.144244  0.10  0.6200  1.185  1.7150   \n",
                            "10  2016      8    6  316.0  1.313228  1.065587  0.09  0.5600  1.100  1.6200   \n",
                            "11  2016      8    7  316.0  1.356994  1.078556  0.10  0.6000  1.120  1.7425   \n",
                            "12  2016      8    8  335.0  1.484925  1.131495  0.02  0.6300  1.200  1.9900   \n",
                            "13  2016      8    9  272.0  1.614779  1.164186  0.10  0.8075  1.300  1.9000   \n",
                            "14  2016      8   10  329.0  1.404742  1.038701  0.02  0.7700  1.170  1.7400   \n",
                            "15  2016      8   11  356.0  1.390534  1.159147  0.04  0.6775  1.100  1.7000   \n",
                            "16  2016      8   12  326.0  1.533282  1.158696  0.04  0.7400  1.200  1.9000   \n",
                            "17  2016      8   13  284.0  1.421901  1.080338  0.10  0.7000  1.105  1.7775   \n",
                            "18  2016      8   14  231.0  1.692684  1.372191  0.05  0.8200  1.200  1.9000   \n",
                            "19  2016      8   15  222.0  1.583964  1.157553  0.07  0.8550  1.300  1.8400   \n",
                            "20  2016      8   16  223.0  1.629910  1.223131  0.10  0.7300  1.300  2.0000   \n",
                            "21  2016      8   17  220.0  1.583682  1.203617  0.10  0.8000  1.210  1.9675   \n",
                            "22  2016      8   18  219.0  1.499772  1.159497  0.04  0.7600  1.200  1.8050   \n",
                            "23  2016      8   19  226.0  1.819469  1.416291  0.11  0.8925  1.340  2.1900   \n",
                            "24  2016      8   20  237.0  1.553207  1.296262  0.02  0.7000  1.200  2.0000   \n",
                            "25  2016      8   21  266.0  1.332368  1.032210  0.03  0.6050  1.140  1.6925   \n",
                            "26  2016      8   22  215.0  1.451488  1.185657  0.01  0.7000  1.180  1.8000   \n",
                            "27  2016      8   23  233.0  1.643391  1.245661  0.04  0.8200  1.300  2.1000   \n",
                            "28  2016      8   24  216.0  1.553194  1.144054  0.03  0.8375  1.290  1.9000   \n",
                            "29  2016      8   25  238.0  1.519328  0.926028  0.10  0.8900  1.400  1.9950   \n",
                            "\n",
                            "     max  \n",
                            "0   5.60  \n",
                            "1   5.10  \n",
                            "2   7.70  \n",
                            "3   5.70  \n",
                            "4   5.90  \n",
                            "5   6.10  \n",
                            "6   5.50  \n",
                            "7   5.10  \n",
                            "8   6.30  \n",
                            "9   5.70  \n",
                            "10  5.40  \n",
                            "11  5.10  \n",
                            "12  5.10  \n",
                            "13  5.09  \n",
                            "14  5.40  \n",
                            "15  7.20  \n",
                            "16  5.40  \n",
                            "17  5.20  \n",
                            "18  5.90  \n",
                            "19  5.40  \n",
                            "20  5.10  \n",
                            "21  5.20  \n",
                            "22  5.90  \n",
                            "23  7.40  \n",
                            "24  6.40  \n",
                            "25  5.10  \n",
                            "26  5.60  \n",
                            "27  6.20  \n",
                            "28  6.80  \n",
                            "29  5.90  "
                        ]
                    },
                    "execution_count": 46,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "magnitudes_reset = magnitudes.reset_index()\n",
                "magnitudes_reset"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "You could optionally pass in the name of an index level to turn it into a column instead. Take a look at the following:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 48,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/html": [
                            "<div>\n",
                            "<style scoped>\n",
                            "    .dataframe tbody tr th:only-of-type {\n",
                            "        vertical-align: middle;\n",
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                            "\n",
                            "    .dataframe tbody tr th {\n",
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                            "\n",
                            "    .dataframe thead th {\n",
                            "        text-align: right;\n",
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                            "</style>\n",
                            "<table border=\"1\" class=\"dataframe\">\n",
                            "  <thead>\n",
                            "    <tr style=\"text-align: right;\">\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th>year</th>\n",
                            "      <th>count</th>\n",
                            "      <th>mean</th>\n",
                            "      <th>std</th>\n",
                            "      <th>min</th>\n",
                            "      <th>25%</th>\n",
                            "      <th>50%</th>\n",
                            "      <th>75%</th>\n",
                            "      <th>max</th>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>month</th>\n",
                            "      <th>day</th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "    </tr>\n",
                            "  </thead>\n",
                            "  <tbody>\n",
                            "    <tr>\n",
                            "      <th rowspan=\"5\" valign=\"top\">7</th>\n",
                            "      <th>27</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>272.0</td>\n",
                            "      <td>1.617574</td>\n",
                            "      <td>1.095349</td>\n",
                            "      <td>0.06</td>\n",
                            "      <td>0.9000</td>\n",
                            "      <td>1.400</td>\n",
                            "      <td>2.0000</td>\n",
                            "      <td>5.60</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>28</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>308.0</td>\n",
                            "      <td>1.448149</td>\n",
                            "      <td>0.896851</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.8775</td>\n",
                            "      <td>1.240</td>\n",
                            "      <td>1.8000</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>29</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>309.0</td>\n",
                            "      <td>1.640129</td>\n",
                            "      <td>1.165952</td>\n",
                            "      <td>0.01</td>\n",
                            "      <td>0.8800</td>\n",
                            "      <td>1.450</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>7.70</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>30</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>329.0</td>\n",
                            "      <td>1.615076</td>\n",
                            "      <td>1.262618</td>\n",
                            "      <td>0.03</td>\n",
                            "      <td>0.7000</td>\n",
                            "      <td>1.240</td>\n",
                            "      <td>2.0000</td>\n",
                            "      <td>5.70</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>31</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>278.0</td>\n",
                            "      <td>1.750827</td>\n",
                            "      <td>1.261577</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.9000</td>\n",
                            "      <td>1.500</td>\n",
                            "      <td>2.1475</td>\n",
                            "      <td>5.90</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th rowspan=\"25\" valign=\"top\">8</th>\n",
                            "      <th>1</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>356.0</td>\n",
                            "      <td>1.520056</td>\n",
                            "      <td>1.157326</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.8000</td>\n",
                            "      <td>1.245</td>\n",
                            "      <td>1.8025</td>\n",
                            "      <td>6.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>2</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>292.0</td>\n",
                            "      <td>1.539418</td>\n",
                            "      <td>1.089946</td>\n",
                            "      <td>0.05</td>\n",
                            "      <td>0.8000</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>5.50</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>3</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>294.0</td>\n",
                            "      <td>1.556327</td>\n",
                            "      <td>1.147365</td>\n",
                            "      <td>0.01</td>\n",
                            "      <td>0.8300</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.8150</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>4</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>420.0</td>\n",
                            "      <td>1.249190</td>\n",
                            "      <td>1.034738</td>\n",
                            "      <td>0.05</td>\n",
                            "      <td>0.6000</td>\n",
                            "      <td>1.000</td>\n",
                            "      <td>1.5825</td>\n",
                            "      <td>6.30</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>5</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>256.0</td>\n",
                            "      <td>1.428789</td>\n",
                            "      <td>1.144244</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.6200</td>\n",
                            "      <td>1.185</td>\n",
                            "      <td>1.7150</td>\n",
                            "      <td>5.70</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>6</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>316.0</td>\n",
                            "      <td>1.313228</td>\n",
                            "      <td>1.065587</td>\n",
                            "      <td>0.09</td>\n",
                            "      <td>0.5600</td>\n",
                            "      <td>1.100</td>\n",
                            "      <td>1.6200</td>\n",
                            "      <td>5.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>7</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>316.0</td>\n",
                            "      <td>1.356994</td>\n",
                            "      <td>1.078556</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.6000</td>\n",
                            "      <td>1.120</td>\n",
                            "      <td>1.7425</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>335.0</td>\n",
                            "      <td>1.484925</td>\n",
                            "      <td>1.131495</td>\n",
                            "      <td>0.02</td>\n",
                            "      <td>0.6300</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.9900</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>9</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>272.0</td>\n",
                            "      <td>1.614779</td>\n",
                            "      <td>1.164186</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.8075</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>5.09</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>10</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>329.0</td>\n",
                            "      <td>1.404742</td>\n",
                            "      <td>1.038701</td>\n",
                            "      <td>0.02</td>\n",
                            "      <td>0.7700</td>\n",
                            "      <td>1.170</td>\n",
                            "      <td>1.7400</td>\n",
                            "      <td>5.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>11</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>356.0</td>\n",
                            "      <td>1.390534</td>\n",
                            "      <td>1.159147</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.6775</td>\n",
                            "      <td>1.100</td>\n",
                            "      <td>1.7000</td>\n",
                            "      <td>7.20</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>12</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>326.0</td>\n",
                            "      <td>1.533282</td>\n",
                            "      <td>1.158696</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.7400</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>5.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>13</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>284.0</td>\n",
                            "      <td>1.421901</td>\n",
                            "      <td>1.080338</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.7000</td>\n",
                            "      <td>1.105</td>\n",
                            "      <td>1.7775</td>\n",
                            "      <td>5.20</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>14</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>231.0</td>\n",
                            "      <td>1.692684</td>\n",
                            "      <td>1.372191</td>\n",
                            "      <td>0.05</td>\n",
                            "      <td>0.8200</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>5.90</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>15</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>222.0</td>\n",
                            "      <td>1.583964</td>\n",
                            "      <td>1.157553</td>\n",
                            "      <td>0.07</td>\n",
                            "      <td>0.8550</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>1.8400</td>\n",
                            "      <td>5.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>16</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>223.0</td>\n",
                            "      <td>1.629910</td>\n",
                            "      <td>1.223131</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.7300</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>2.0000</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>17</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>220.0</td>\n",
                            "      <td>1.583682</td>\n",
                            "      <td>1.203617</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.8000</td>\n",
                            "      <td>1.210</td>\n",
                            "      <td>1.9675</td>\n",
                            "      <td>5.20</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>18</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>219.0</td>\n",
                            "      <td>1.499772</td>\n",
                            "      <td>1.159497</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.7600</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.8050</td>\n",
                            "      <td>5.90</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>19</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>226.0</td>\n",
                            "      <td>1.819469</td>\n",
                            "      <td>1.416291</td>\n",
                            "      <td>0.11</td>\n",
                            "      <td>0.8925</td>\n",
                            "      <td>1.340</td>\n",
                            "      <td>2.1900</td>\n",
                            "      <td>7.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>20</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>237.0</td>\n",
                            "      <td>1.553207</td>\n",
                            "      <td>1.296262</td>\n",
                            "      <td>0.02</td>\n",
                            "      <td>0.7000</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>2.0000</td>\n",
                            "      <td>6.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>21</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>266.0</td>\n",
                            "      <td>1.332368</td>\n",
                            "      <td>1.032210</td>\n",
                            "      <td>0.03</td>\n",
                            "      <td>0.6050</td>\n",
                            "      <td>1.140</td>\n",
                            "      <td>1.6925</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>22</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>215.0</td>\n",
                            "      <td>1.451488</td>\n",
                            "      <td>1.185657</td>\n",
                            "      <td>0.01</td>\n",
                            "      <td>0.7000</td>\n",
                            "      <td>1.180</td>\n",
                            "      <td>1.8000</td>\n",
                            "      <td>5.60</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>23</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>233.0</td>\n",
                            "      <td>1.643391</td>\n",
                            "      <td>1.245661</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.8200</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>2.1000</td>\n",
                            "      <td>6.20</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>24</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>216.0</td>\n",
                            "      <td>1.553194</td>\n",
                            "      <td>1.144054</td>\n",
                            "      <td>0.03</td>\n",
                            "      <td>0.8375</td>\n",
                            "      <td>1.290</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>6.80</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>25</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>238.0</td>\n",
                            "      <td>1.519328</td>\n",
                            "      <td>0.926028</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.8900</td>\n",
                            "      <td>1.400</td>\n",
                            "      <td>1.9950</td>\n",
                            "      <td>5.90</td>\n",
                            "    </tr>\n",
                            "  </tbody>\n",
                            "</table>\n",
                            "</div>"
                        ],
                        "text/plain": [
                            "           year  count      mean       std   min     25%    50%     75%   max\n",
                            "month day                                                                    \n",
                            "7     27   2016  272.0  1.617574  1.095349  0.06  0.9000  1.400  2.0000  5.60\n",
                            "      28   2016  308.0  1.448149  0.896851  0.10  0.8775  1.240  1.8000  5.10\n",
                            "      29   2016  309.0  1.640129  1.165952  0.01  0.8800  1.450  1.9000  7.70\n",
                            "      30   2016  329.0  1.615076  1.262618  0.03  0.7000  1.240  2.0000  5.70\n",
                            "      31   2016  278.0  1.750827  1.261577  0.10  0.9000  1.500  2.1475  5.90\n",
                            "8     1    2016  356.0  1.520056  1.157326  0.04  0.8000  1.245  1.8025  6.10\n",
                            "      2    2016  292.0  1.539418  1.089946  0.05  0.8000  1.300  1.9000  5.50\n",
                            "      3    2016  294.0  1.556327  1.147365  0.01  0.8300  1.200  1.8150  5.10\n",
                            "      4    2016  420.0  1.249190  1.034738  0.05  0.6000  1.000  1.5825  6.30\n",
                            "      5    2016  256.0  1.428789  1.144244  0.10  0.6200  1.185  1.7150  5.70\n",
                            "      6    2016  316.0  1.313228  1.065587  0.09  0.5600  1.100  1.6200  5.40\n",
                            "      7    2016  316.0  1.356994  1.078556  0.10  0.6000  1.120  1.7425  5.10\n",
                            "      8    2016  335.0  1.484925  1.131495  0.02  0.6300  1.200  1.9900  5.10\n",
                            "      9    2016  272.0  1.614779  1.164186  0.10  0.8075  1.300  1.9000  5.09\n",
                            "      10   2016  329.0  1.404742  1.038701  0.02  0.7700  1.170  1.7400  5.40\n",
                            "      11   2016  356.0  1.390534  1.159147  0.04  0.6775  1.100  1.7000  7.20\n",
                            "      12   2016  326.0  1.533282  1.158696  0.04  0.7400  1.200  1.9000  5.40\n",
                            "      13   2016  284.0  1.421901  1.080338  0.10  0.7000  1.105  1.7775  5.20\n",
                            "      14   2016  231.0  1.692684  1.372191  0.05  0.8200  1.200  1.9000  5.90\n",
                            "      15   2016  222.0  1.583964  1.157553  0.07  0.8550  1.300  1.8400  5.40\n",
                            "      16   2016  223.0  1.629910  1.223131  0.10  0.7300  1.300  2.0000  5.10\n",
                            "      17   2016  220.0  1.583682  1.203617  0.10  0.8000  1.210  1.9675  5.20\n",
                            "      18   2016  219.0  1.499772  1.159497  0.04  0.7600  1.200  1.8050  5.90\n",
                            "      19   2016  226.0  1.819469  1.416291  0.11  0.8925  1.340  2.1900  7.40\n",
                            "      20   2016  237.0  1.553207  1.296262  0.02  0.7000  1.200  2.0000  6.40\n",
                            "      21   2016  266.0  1.332368  1.032210  0.03  0.6050  1.140  1.6925  5.10\n",
                            "      22   2016  215.0  1.451488  1.185657  0.01  0.7000  1.180  1.8000  5.60\n",
                            "      23   2016  233.0  1.643391  1.245661  0.04  0.8200  1.300  2.1000  6.20\n",
                            "      24   2016  216.0  1.553194  1.144054  0.03  0.8375  1.290  1.9000  6.80\n",
                            "      25   2016  238.0  1.519328  0.926028  0.10  0.8900  1.400  1.9950  5.90"
                        ]
                    },
                    "execution_count": 48,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "magnitudes_year_reset = magnitudes.reset_index(level=\"year\")\n",
                "magnitudes_year_reset"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 49,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/html": [
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                            "<table border=\"1\" class=\"dataframe\">\n",
                            "  <thead>\n",
                            "    <tr style=\"text-align: right;\">\n",
                            "      <th></th>\n",
                            "      <th>year</th>\n",
                            "      <th>day</th>\n",
                            "      <th>count</th>\n",
                            "      <th>mean</th>\n",
                            "      <th>std</th>\n",
                            "      <th>min</th>\n",
                            "      <th>25%</th>\n",
                            "      <th>50%</th>\n",
                            "      <th>75%</th>\n",
                            "      <th>max</th>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>month</th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "      <th></th>\n",
                            "    </tr>\n",
                            "  </thead>\n",
                            "  <tbody>\n",
                            "    <tr>\n",
                            "      <th>7</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>27</td>\n",
                            "      <td>272.0</td>\n",
                            "      <td>1.617574</td>\n",
                            "      <td>1.095349</td>\n",
                            "      <td>0.06</td>\n",
                            "      <td>0.9000</td>\n",
                            "      <td>1.400</td>\n",
                            "      <td>2.0000</td>\n",
                            "      <td>5.60</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>7</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>28</td>\n",
                            "      <td>308.0</td>\n",
                            "      <td>1.448149</td>\n",
                            "      <td>0.896851</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.8775</td>\n",
                            "      <td>1.240</td>\n",
                            "      <td>1.8000</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>7</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>29</td>\n",
                            "      <td>309.0</td>\n",
                            "      <td>1.640129</td>\n",
                            "      <td>1.165952</td>\n",
                            "      <td>0.01</td>\n",
                            "      <td>0.8800</td>\n",
                            "      <td>1.450</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>7.70</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>7</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>30</td>\n",
                            "      <td>329.0</td>\n",
                            "      <td>1.615076</td>\n",
                            "      <td>1.262618</td>\n",
                            "      <td>0.03</td>\n",
                            "      <td>0.7000</td>\n",
                            "      <td>1.240</td>\n",
                            "      <td>2.0000</td>\n",
                            "      <td>5.70</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>7</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>31</td>\n",
                            "      <td>278.0</td>\n",
                            "      <td>1.750827</td>\n",
                            "      <td>1.261577</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.9000</td>\n",
                            "      <td>1.500</td>\n",
                            "      <td>2.1475</td>\n",
                            "      <td>5.90</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>1</td>\n",
                            "      <td>356.0</td>\n",
                            "      <td>1.520056</td>\n",
                            "      <td>1.157326</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.8000</td>\n",
                            "      <td>1.245</td>\n",
                            "      <td>1.8025</td>\n",
                            "      <td>6.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>2</td>\n",
                            "      <td>292.0</td>\n",
                            "      <td>1.539418</td>\n",
                            "      <td>1.089946</td>\n",
                            "      <td>0.05</td>\n",
                            "      <td>0.8000</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>5.50</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>3</td>\n",
                            "      <td>294.0</td>\n",
                            "      <td>1.556327</td>\n",
                            "      <td>1.147365</td>\n",
                            "      <td>0.01</td>\n",
                            "      <td>0.8300</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.8150</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>4</td>\n",
                            "      <td>420.0</td>\n",
                            "      <td>1.249190</td>\n",
                            "      <td>1.034738</td>\n",
                            "      <td>0.05</td>\n",
                            "      <td>0.6000</td>\n",
                            "      <td>1.000</td>\n",
                            "      <td>1.5825</td>\n",
                            "      <td>6.30</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>5</td>\n",
                            "      <td>256.0</td>\n",
                            "      <td>1.428789</td>\n",
                            "      <td>1.144244</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.6200</td>\n",
                            "      <td>1.185</td>\n",
                            "      <td>1.7150</td>\n",
                            "      <td>5.70</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>6</td>\n",
                            "      <td>316.0</td>\n",
                            "      <td>1.313228</td>\n",
                            "      <td>1.065587</td>\n",
                            "      <td>0.09</td>\n",
                            "      <td>0.5600</td>\n",
                            "      <td>1.100</td>\n",
                            "      <td>1.6200</td>\n",
                            "      <td>5.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>7</td>\n",
                            "      <td>316.0</td>\n",
                            "      <td>1.356994</td>\n",
                            "      <td>1.078556</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.6000</td>\n",
                            "      <td>1.120</td>\n",
                            "      <td>1.7425</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>8</td>\n",
                            "      <td>335.0</td>\n",
                            "      <td>1.484925</td>\n",
                            "      <td>1.131495</td>\n",
                            "      <td>0.02</td>\n",
                            "      <td>0.6300</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.9900</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>9</td>\n",
                            "      <td>272.0</td>\n",
                            "      <td>1.614779</td>\n",
                            "      <td>1.164186</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.8075</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>5.09</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>10</td>\n",
                            "      <td>329.0</td>\n",
                            "      <td>1.404742</td>\n",
                            "      <td>1.038701</td>\n",
                            "      <td>0.02</td>\n",
                            "      <td>0.7700</td>\n",
                            "      <td>1.170</td>\n",
                            "      <td>1.7400</td>\n",
                            "      <td>5.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>11</td>\n",
                            "      <td>356.0</td>\n",
                            "      <td>1.390534</td>\n",
                            "      <td>1.159147</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.6775</td>\n",
                            "      <td>1.100</td>\n",
                            "      <td>1.7000</td>\n",
                            "      <td>7.20</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>12</td>\n",
                            "      <td>326.0</td>\n",
                            "      <td>1.533282</td>\n",
                            "      <td>1.158696</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.7400</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>5.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>13</td>\n",
                            "      <td>284.0</td>\n",
                            "      <td>1.421901</td>\n",
                            "      <td>1.080338</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.7000</td>\n",
                            "      <td>1.105</td>\n",
                            "      <td>1.7775</td>\n",
                            "      <td>5.20</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>14</td>\n",
                            "      <td>231.0</td>\n",
                            "      <td>1.692684</td>\n",
                            "      <td>1.372191</td>\n",
                            "      <td>0.05</td>\n",
                            "      <td>0.8200</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>5.90</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>15</td>\n",
                            "      <td>222.0</td>\n",
                            "      <td>1.583964</td>\n",
                            "      <td>1.157553</td>\n",
                            "      <td>0.07</td>\n",
                            "      <td>0.8550</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>1.8400</td>\n",
                            "      <td>5.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>16</td>\n",
                            "      <td>223.0</td>\n",
                            "      <td>1.629910</td>\n",
                            "      <td>1.223131</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.7300</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>2.0000</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>17</td>\n",
                            "      <td>220.0</td>\n",
                            "      <td>1.583682</td>\n",
                            "      <td>1.203617</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.8000</td>\n",
                            "      <td>1.210</td>\n",
                            "      <td>1.9675</td>\n",
                            "      <td>5.20</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>18</td>\n",
                            "      <td>219.0</td>\n",
                            "      <td>1.499772</td>\n",
                            "      <td>1.159497</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.7600</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>1.8050</td>\n",
                            "      <td>5.90</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>19</td>\n",
                            "      <td>226.0</td>\n",
                            "      <td>1.819469</td>\n",
                            "      <td>1.416291</td>\n",
                            "      <td>0.11</td>\n",
                            "      <td>0.8925</td>\n",
                            "      <td>1.340</td>\n",
                            "      <td>2.1900</td>\n",
                            "      <td>7.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>20</td>\n",
                            "      <td>237.0</td>\n",
                            "      <td>1.553207</td>\n",
                            "      <td>1.296262</td>\n",
                            "      <td>0.02</td>\n",
                            "      <td>0.7000</td>\n",
                            "      <td>1.200</td>\n",
                            "      <td>2.0000</td>\n",
                            "      <td>6.40</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>21</td>\n",
                            "      <td>266.0</td>\n",
                            "      <td>1.332368</td>\n",
                            "      <td>1.032210</td>\n",
                            "      <td>0.03</td>\n",
                            "      <td>0.6050</td>\n",
                            "      <td>1.140</td>\n",
                            "      <td>1.6925</td>\n",
                            "      <td>5.10</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>22</td>\n",
                            "      <td>215.0</td>\n",
                            "      <td>1.451488</td>\n",
                            "      <td>1.185657</td>\n",
                            "      <td>0.01</td>\n",
                            "      <td>0.7000</td>\n",
                            "      <td>1.180</td>\n",
                            "      <td>1.8000</td>\n",
                            "      <td>5.60</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>23</td>\n",
                            "      <td>233.0</td>\n",
                            "      <td>1.643391</td>\n",
                            "      <td>1.245661</td>\n",
                            "      <td>0.04</td>\n",
                            "      <td>0.8200</td>\n",
                            "      <td>1.300</td>\n",
                            "      <td>2.1000</td>\n",
                            "      <td>6.20</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>24</td>\n",
                            "      <td>216.0</td>\n",
                            "      <td>1.553194</td>\n",
                            "      <td>1.144054</td>\n",
                            "      <td>0.03</td>\n",
                            "      <td>0.8375</td>\n",
                            "      <td>1.290</td>\n",
                            "      <td>1.9000</td>\n",
                            "      <td>6.80</td>\n",
                            "    </tr>\n",
                            "    <tr>\n",
                            "      <th>8</th>\n",
                            "      <td>2016</td>\n",
                            "      <td>25</td>\n",
                            "      <td>238.0</td>\n",
                            "      <td>1.519328</td>\n",
                            "      <td>0.926028</td>\n",
                            "      <td>0.10</td>\n",
                            "      <td>0.8900</td>\n",
                            "      <td>1.400</td>\n",
                            "      <td>1.9950</td>\n",
                            "      <td>5.90</td>\n",
                            "    </tr>\n",
                            "  </tbody>\n",
                            "</table>\n",
                            "</div>"
                        ],
                        "text/plain": [
                            "       year  day  count      mean       std   min     25%    50%     75%   max\n",
                            "month                                                                         \n",
                            "7      2016   27  272.0  1.617574  1.095349  0.06  0.9000  1.400  2.0000  5.60\n",
                            "7      2016   28  308.0  1.448149  0.896851  0.10  0.8775  1.240  1.8000  5.10\n",
                            "7      2016   29  309.0  1.640129  1.165952  0.01  0.8800  1.450  1.9000  7.70\n",
                            "7      2016   30  329.0  1.615076  1.262618  0.03  0.7000  1.240  2.0000  5.70\n",
                            "7      2016   31  278.0  1.750827  1.261577  0.10  0.9000  1.500  2.1475  5.90\n",
                            "8      2016    1  356.0  1.520056  1.157326  0.04  0.8000  1.245  1.8025  6.10\n",
                            "8      2016    2  292.0  1.539418  1.089946  0.05  0.8000  1.300  1.9000  5.50\n",
                            "8      2016    3  294.0  1.556327  1.147365  0.01  0.8300  1.200  1.8150  5.10\n",
                            "8      2016    4  420.0  1.249190  1.034738  0.05  0.6000  1.000  1.5825  6.30\n",
                            "8      2016    5  256.0  1.428789  1.144244  0.10  0.6200  1.185  1.7150  5.70\n",
                            "8      2016    6  316.0  1.313228  1.065587  0.09  0.5600  1.100  1.6200  5.40\n",
                            "8      2016    7  316.0  1.356994  1.078556  0.10  0.6000  1.120  1.7425  5.10\n",
                            "8      2016    8  335.0  1.484925  1.131495  0.02  0.6300  1.200  1.9900  5.10\n",
                            "8      2016    9  272.0  1.614779  1.164186  0.10  0.8075  1.300  1.9000  5.09\n",
                            "8      2016   10  329.0  1.404742  1.038701  0.02  0.7700  1.170  1.7400  5.40\n",
                            "8      2016   11  356.0  1.390534  1.159147  0.04  0.6775  1.100  1.7000  7.20\n",
                            "8      2016   12  326.0  1.533282  1.158696  0.04  0.7400  1.200  1.9000  5.40\n",
                            "8      2016   13  284.0  1.421901  1.080338  0.10  0.7000  1.105  1.7775  5.20\n",
                            "8      2016   14  231.0  1.692684  1.372191  0.05  0.8200  1.200  1.9000  5.90\n",
                            "8      2016   15  222.0  1.583964  1.157553  0.07  0.8550  1.300  1.8400  5.40\n",
                            "8      2016   16  223.0  1.629910  1.223131  0.10  0.7300  1.300  2.0000  5.10\n",
                            "8      2016   17  220.0  1.583682  1.203617  0.10  0.8000  1.210  1.9675  5.20\n",
                            "8      2016   18  219.0  1.499772  1.159497  0.04  0.7600  1.200  1.8050  5.90\n",
                            "8      2016   19  226.0  1.819469  1.416291  0.11  0.8925  1.340  2.1900  7.40\n",
                            "8      2016   20  237.0  1.553207  1.296262  0.02  0.7000  1.200  2.0000  6.40\n",
                            "8      2016   21  266.0  1.332368  1.032210  0.03  0.6050  1.140  1.6925  5.10\n",
                            "8      2016   22  215.0  1.451488  1.185657  0.01  0.7000  1.180  1.8000  5.60\n",
                            "8      2016   23  233.0  1.643391  1.245661  0.04  0.8200  1.300  2.1000  6.20\n",
                            "8      2016   24  216.0  1.553194  1.144054  0.03  0.8375  1.290  1.9000  6.80\n",
                            "8      2016   25  238.0  1.519328  0.926028  0.10  0.8900  1.400  1.9950  5.90"
                        ]
                    },
                    "execution_count": 49,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "magnitudes_day_year_reset = magnitudes.reset_index(level=[\"year\", \"day\"])\n",
                "magnitudes_day_year_reset"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "**Food for thought:** When might it be preferable to use a `MultiIndex`? When might it not be preferable?"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "## ⏸️ Pause and 🧠 Think\n",
                "\n",
                "Take a moment to review the following concepts and reflect on your own understanding. A good temperature check for your understanding is asking yourself whether you might be able to explain these concepts to a friend outside of this class.\n",
                "\n",
                "Here's what we covered in this lesson:\n",
                "\n",
                "* `groupby`\n",
                "* `apply`\n",
                "* Hierarchical indexing and `MultiIndex`\n",
                "\n",
                "Here are some other guiding exercises and questions to help you reflect on what you've seen so far:\n",
                "\n",
                "1. In your own words, write a few sentences summarizing what you learned in this lesson.\n",
                "2. What did you find challenging in this lesson? Come up with some questions you might ask your peers or the course staff to help you better understand that concept.\n",
                "3. What was familiar about what you saw in this lesson? How might you relate it to things you have learned before?\n",
                "4. Throughout the lesson, there were a few **Food for thought** questions. Try exploring one or more of them and see what you find.\n",
                "\n",
                "## In-Class\n",
                "\n",
                "When you come to class, we will work together on the problems in `ufos.ipynb`. We will also need `ufos.csv` for these tasks. Make sure that you have a way of editing and running these files!\n",
                "\n",
                "## Canvas Quiz\n",
                "\n",
                "All done with the lesson? Complete the [<u>Canvas Quiz linked here!</u>](https://canvas.uw.edu/courses/1860345/quizzes/2334842)\n"
            ]
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