11-DA_Pandas_splitting.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 11. Splitting data "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Often one has tables that mix regular variables (e.g. the size of cells in microscopy images) with categorical variables (e.g. the type of cell to which they belong). In that case, it is quite usual to split the data by categories or *groups* to do computations. Pandas allows to do this very easily. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 11.1 Grouping"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's import some data and have a look at them:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "composers = pd.read_excel('Data/composers.xlsx', sheet_name='Sheet5')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>composer</th>\n",
       "      <th>birth</th>\n",
       "      <th>death</th>\n",
       "      <th>period</th>\n",
       "      <th>country</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Mahler</td>\n",
       "      <td>1860</td>\n",
       "      <td>1911.0</td>\n",
       "      <td>post-romantic</td>\n",
       "      <td>Austria</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Beethoven</td>\n",
       "      <td>1770</td>\n",
       "      <td>1827.0</td>\n",
       "      <td>romantic</td>\n",
       "      <td>Germany</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Puccini</td>\n",
       "      <td>1858</td>\n",
       "      <td>1924.0</td>\n",
       "      <td>post-romantic</td>\n",
       "      <td>Italy</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Shostakovich</td>\n",
       "      <td>1906</td>\n",
       "      <td>1975.0</td>\n",
       "      <td>modern</td>\n",
       "      <td>Russia</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Verdi</td>\n",
       "      <td>1813</td>\n",
       "      <td>1901.0</td>\n",
       "      <td>romantic</td>\n",
       "      <td>Italy</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       composer  birth   death         period  country\n",
       "0        Mahler   1860  1911.0  post-romantic  Austria\n",
       "1     Beethoven   1770  1827.0       romantic  Germany\n",
       "2       Puccini   1858  1924.0  post-romantic    Italy\n",
       "3  Shostakovich   1906  1975.0         modern   Russia\n",
       "4         Verdi   1813  1901.0       romantic    Italy"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "composers.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also add a column here to calculate the composers' age:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "composers['age'] = composers.death - composers.birth"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 11.1.1 Single level \n",
    "What if we want now to count how many composers we have in a certain category like the period or country? In classical computing we would maybe do a for loop to count occurrences. Pandas simplifies this with the ```groupby()``` function, which actually groups elements by a certain criteria, e.g. a categorical variable like the period:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pandas.core.groupby.generic.DataFrameGroupBy object at 0x11d2fc850>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "composer_grouped = composers.groupby('period')\n",
    "composer_grouped"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The output is a bit cryptic. What we actually have is a new object called a group which has a lot of handy properties. First let's see what the groups actually are. We can find all groups with ```groups```:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'baroque': Int64Index([14, 16, 17, 20, 21, 28, 29, 30, 31, 47], dtype='int64'),\n",
       " 'classic': Int64Index([9, 10, 32, 40, 51], dtype='int64'),\n",
       " 'modern': Int64Index([3, 7, 11, 12, 19, 25, 45, 46, 50, 53, 54, 55, 56], dtype='int64'),\n",
       " 'post-romantic': Int64Index([0, 2, 8, 18, 49], dtype='int64'),\n",
       " 'renaissance': Int64Index([13, 26, 27, 36, 37, 43, 44], dtype='int64'),\n",
       " 'romantic': Int64Index([1, 4, 5, 6, 15, 22, 23, 24, 33, 34, 35, 38, 39, 41, 42, 48, 52], dtype='int64')}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "composer_grouped.groups"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have a dictionary, where each *period* that appears in the Dataframe is a key and each key contains a list of dataframe *indices* of rows with those periods. We will rarely directly use those indices, as most operations on groups only use those \"behind the scene\".\n",
    "\n",
    "For example we can use ```describe()``` on a group object, just like we did it before for a Dataframe:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
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       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
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       "      <th>mean</th>\n",
       "      <th>...</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
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       "      <th>std</th>\n",
       "      <th>min</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>baroque</th>\n",
       "      <td>10.0</td>\n",
       "      <td>1663.300000</td>\n",
       "      <td>36.009412</td>\n",
       "      <td>1587.0</td>\n",
       "      <td>1647.0</td>\n",
       "      <td>1676.5</td>\n",
       "      <td>1685.0</td>\n",
       "      <td>1710.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>1720.200000</td>\n",
       "      <td>...</td>\n",
       "      <td>1755.25</td>\n",
       "      <td>1764.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>56.900000</td>\n",
       "      <td>18.716897</td>\n",
       "      <td>26.0</td>\n",
       "      <td>40.25</td>\n",
       "      <td>63.0</td>\n",
       "      <td>70.5</td>\n",
       "      <td>81.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>classic</th>\n",
       "      <td>5.0</td>\n",
       "      <td>1744.400000</td>\n",
       "      <td>12.054045</td>\n",
       "      <td>1731.0</td>\n",
       "      <td>1732.0</td>\n",
       "      <td>1749.0</td>\n",
       "      <td>1754.0</td>\n",
       "      <td>1756.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1801.200000</td>\n",
       "      <td>...</td>\n",
       "      <td>1806.00</td>\n",
       "      <td>1809.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>56.800000</td>\n",
       "      <td>16.238842</td>\n",
       "      <td>35.0</td>\n",
       "      <td>52.00</td>\n",
       "      <td>52.0</td>\n",
       "      <td>68.0</td>\n",
       "      <td>77.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>modern</th>\n",
       "      <td>13.0</td>\n",
       "      <td>1905.692308</td>\n",
       "      <td>28.595992</td>\n",
       "      <td>1854.0</td>\n",
       "      <td>1891.0</td>\n",
       "      <td>1902.0</td>\n",
       "      <td>1918.0</td>\n",
       "      <td>1971.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>1974.090909</td>\n",
       "      <td>...</td>\n",
       "      <td>1990.00</td>\n",
       "      <td>2016.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>77.181818</td>\n",
       "      <td>13.136348</td>\n",
       "      <td>50.0</td>\n",
       "      <td>70.50</td>\n",
       "      <td>81.0</td>\n",
       "      <td>88.0</td>\n",
       "      <td>91.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>post-romantic</th>\n",
       "      <td>5.0</td>\n",
       "      <td>1854.200000</td>\n",
       "      <td>17.123084</td>\n",
       "      <td>1824.0</td>\n",
       "      <td>1858.0</td>\n",
       "      <td>1860.0</td>\n",
       "      <td>1864.0</td>\n",
       "      <td>1865.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1927.400000</td>\n",
       "      <td>...</td>\n",
       "      <td>1949.00</td>\n",
       "      <td>1957.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>73.200000</td>\n",
       "      <td>16.115210</td>\n",
       "      <td>51.0</td>\n",
       "      <td>66.00</td>\n",
       "      <td>72.0</td>\n",
       "      <td>85.0</td>\n",
       "      <td>92.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>renaissance</th>\n",
       "      <td>7.0</td>\n",
       "      <td>1527.142857</td>\n",
       "      <td>59.881629</td>\n",
       "      <td>1397.0</td>\n",
       "      <td>1528.5</td>\n",
       "      <td>1540.0</td>\n",
       "      <td>1564.5</td>\n",
       "      <td>1567.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>1595.285714</td>\n",
       "      <td>...</td>\n",
       "      <td>1624.50</td>\n",
       "      <td>1643.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>68.142857</td>\n",
       "      <td>12.061351</td>\n",
       "      <td>47.0</td>\n",
       "      <td>62.50</td>\n",
       "      <td>69.0</td>\n",
       "      <td>76.5</td>\n",
       "      <td>83.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>romantic</th>\n",
       "      <td>17.0</td>\n",
       "      <td>1824.823529</td>\n",
       "      <td>25.468695</td>\n",
       "      <td>1770.0</td>\n",
       "      <td>1810.0</td>\n",
       "      <td>1824.0</td>\n",
       "      <td>1841.0</td>\n",
       "      <td>1867.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>1883.588235</td>\n",
       "      <td>...</td>\n",
       "      <td>1904.00</td>\n",
       "      <td>1919.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>58.764706</td>\n",
       "      <td>13.250139</td>\n",
       "      <td>34.0</td>\n",
       "      <td>49.00</td>\n",
       "      <td>60.0</td>\n",
       "      <td>66.0</td>\n",
       "      <td>88.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>6 rows × 24 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              birth                                                          \\\n",
       "              count         mean        std     min     25%     50%     75%   \n",
       "period                                                                        \n",
       "baroque        10.0  1663.300000  36.009412  1587.0  1647.0  1676.5  1685.0   \n",
       "classic         5.0  1744.400000  12.054045  1731.0  1732.0  1749.0  1754.0   \n",
       "modern         13.0  1905.692308  28.595992  1854.0  1891.0  1902.0  1918.0   \n",
       "post-romantic   5.0  1854.200000  17.123084  1824.0  1858.0  1860.0  1864.0   \n",
       "renaissance     7.0  1527.142857  59.881629  1397.0  1528.5  1540.0  1564.5   \n",
       "romantic       17.0  1824.823529  25.468695  1770.0  1810.0  1824.0  1841.0   \n",
       "\n",
       "                      death               ...                    age  \\\n",
       "                  max count         mean  ...      75%     max count   \n",
       "period                                    ...                          \n",
       "baroque        1710.0  10.0  1720.200000  ...  1755.25  1764.0  10.0   \n",
       "classic        1756.0   5.0  1801.200000  ...  1806.00  1809.0   5.0   \n",
       "modern         1971.0  11.0  1974.090909  ...  1990.00  2016.0  11.0   \n",
       "post-romantic  1865.0   5.0  1927.400000  ...  1949.00  1957.0   5.0   \n",
       "renaissance    1567.0   7.0  1595.285714  ...  1624.50  1643.0   7.0   \n",
       "romantic       1867.0  17.0  1883.588235  ...  1904.00  1919.0  17.0   \n",
       "\n",
       "                                                                    \n",
       "                    mean        std   min    25%   50%   75%   max  \n",
       "period                                                              \n",
       "baroque        56.900000  18.716897  26.0  40.25  63.0  70.5  81.0  \n",
       "classic        56.800000  16.238842  35.0  52.00  52.0  68.0  77.0  \n",
       "modern         77.181818  13.136348  50.0  70.50  81.0  88.0  91.0  \n",
       "post-romantic  73.200000  16.115210  51.0  66.00  72.0  85.0  92.0  \n",
       "renaissance    68.142857  12.061351  47.0  62.50  69.0  76.5  83.0  \n",
       "romantic       58.764706  13.250139  34.0  49.00  60.0  66.0  88.0  \n",
       "\n",
       "[6 rows x 24 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "composer_grouped.describe()#.loc['Austria','birth']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see here that the statistical analysis has been done for each group, the index of each row being the group name (or key in the dictionary). If we are interested in a specific group we can also easily recover it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>composer</th>\n",
       "      <th>birth</th>\n",
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       "      <th>9</th>\n",
       "      <td>Haydn</td>\n",
       "      <td>1732</td>\n",
       "      <td>1809.0</td>\n",
       "      <td>classic</td>\n",
       "      <td>Austria</td>\n",
       "      <td>77.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>Mozart</td>\n",
       "      <td>1756</td>\n",
       "      <td>1791.0</td>\n",
       "      <td>classic</td>\n",
       "      <td>Austria</td>\n",
       "      <td>35.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>Cimarosa</td>\n",
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       "      <td>1801.0</td>\n",
       "      <td>classic</td>\n",
       "      <td>Italy</td>\n",
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       "      <th>40</th>\n",
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       "      <td>Spain</td>\n",
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       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>Dusek</td>\n",
       "      <td>1731</td>\n",
       "      <td>1799.0</td>\n",
       "      <td>classic</td>\n",
       "      <td>Czechia</td>\n",
       "      <td>68.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    composer  birth   death   period  country   age\n",
       "9      Haydn   1732  1809.0  classic  Austria  77.0\n",
       "10    Mozart   1756  1791.0  classic  Austria  35.0\n",
       "32  Cimarosa   1749  1801.0  classic    Italy  52.0\n",
       "40     Soler   1754  1806.0  classic    Spain  52.0\n",
       "51     Dusek   1731  1799.0  classic  Czechia  68.0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "composer_grouped.get_group('classic')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that this returns a sub-group from the original table. Effectively it is almost equivalent to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>composer</th>\n",
       "      <th>birth</th>\n",
       "      <th>death</th>\n",
       "      <th>period</th>\n",
       "      <th>country</th>\n",
       "      <th>age</th>\n",
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       "      <th>9</th>\n",
       "      <td>Haydn</td>\n",
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       "      <td>1809.0</td>\n",
       "      <td>classic</td>\n",
       "      <td>Austria</td>\n",
       "      <td>77.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>Mozart</td>\n",
       "      <td>1756</td>\n",
       "      <td>1791.0</td>\n",
       "      <td>classic</td>\n",
       "      <td>Austria</td>\n",
       "      <td>35.0</td>\n",
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       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>Cimarosa</td>\n",
       "      <td>1749</td>\n",
       "      <td>1801.0</td>\n",
       "      <td>classic</td>\n",
       "      <td>Italy</td>\n",
       "      <td>52.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>Soler</td>\n",
       "      <td>1754</td>\n",
       "      <td>1806.0</td>\n",
       "      <td>classic</td>\n",
       "      <td>Spain</td>\n",
       "      <td>52.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>Dusek</td>\n",
       "      <td>1731</td>\n",
       "      <td>1799.0</td>\n",
       "      <td>classic</td>\n",
       "      <td>Czechia</td>\n",
       "      <td>68.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    composer  birth   death   period  country   age\n",
       "9      Haydn   1732  1809.0  classic  Austria  77.0\n",
       "10    Mozart   1756  1791.0  classic  Austria  35.0\n",
       "32  Cimarosa   1749  1801.0  classic    Italy  52.0\n",
       "40     Soler   1754  1806.0  classic    Spain  52.0\n",
       "51     Dusek   1731  1799.0  classic  Czechia  68.0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "composers[composers.period == 'classic']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 11.1.2 Multi-level\n",
    "\n",
    "If one has multiple categorical variables, one can also do a grouping on several levels. For example here we want to classify composers both by period and country. For this we just give two column names to the ```groupby()``` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"4\" valign=\"top\">baroque</th>\n",
       "      <th>England</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1659.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1659.0</td>\n",
       "      <td>1659.00</td>\n",
       "      <td>1659.0</td>\n",
       "      <td>1659.00</td>\n",
       "      <td>1659.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1695.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>1695.00</td>\n",
       "      <td>1695.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>36.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>36.0</td>\n",
       "      <td>36.00</td>\n",
       "      <td>36.0</td>\n",
       "      <td>36.00</td>\n",
       "      <td>36.0</td>\n",
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       "    <tr>\n",
       "      <th>France</th>\n",
       "      <td>3.0</td>\n",
       "      <td>1650.666667</td>\n",
       "      <td>29.263174</td>\n",
       "      <td>1626.0</td>\n",
       "      <td>1634.50</td>\n",
       "      <td>1643.0</td>\n",
       "      <td>1663.00</td>\n",
       "      <td>1683.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1709.666667</td>\n",
       "      <td>...</td>\n",
       "      <td>1734.00</td>\n",
       "      <td>1764.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>59.000000</td>\n",
       "      <td>23.065125</td>\n",
       "      <td>35.0</td>\n",
       "      <td>48.00</td>\n",
       "      <td>61.0</td>\n",
       "      <td>71.00</td>\n",
       "      <td>81.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Germany</th>\n",
       "      <td>2.0</td>\n",
       "      <td>1685.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1685.0</td>\n",
       "      <td>1685.00</td>\n",
       "      <td>1685.0</td>\n",
       "      <td>1685.00</td>\n",
       "      <td>1685.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1754.500000</td>\n",
       "      <td>...</td>\n",
       "      <td>1756.75</td>\n",
       "      <td>1759.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>69.500000</td>\n",
       "      <td>6.363961</td>\n",
       "      <td>65.0</td>\n",
       "      <td>67.25</td>\n",
       "      <td>69.5</td>\n",
       "      <td>71.75</td>\n",
       "      <td>74.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Italy</th>\n",
       "      <td>4.0</td>\n",
       "      <td>1663.000000</td>\n",
       "      <td>53.285395</td>\n",
       "      <td>1587.0</td>\n",
       "      <td>1649.25</td>\n",
       "      <td>1677.5</td>\n",
       "      <td>1691.25</td>\n",
       "      <td>1710.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1717.250000</td>\n",
       "      <td>...</td>\n",
       "      <td>1741.25</td>\n",
       "      <td>1757.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>54.250000</td>\n",
       "      <td>20.434856</td>\n",
       "      <td>26.0</td>\n",
       "      <td>46.25</td>\n",
       "      <td>59.5</td>\n",
       "      <td>67.50</td>\n",
       "      <td>72.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"4\" valign=\"top\">classic</th>\n",
       "      <th>Austria</th>\n",
       "      <td>2.0</td>\n",
       "      <td>1744.000000</td>\n",
       "      <td>16.970563</td>\n",
       "      <td>1732.0</td>\n",
       "      <td>1738.00</td>\n",
       "      <td>1744.0</td>\n",
       "      <td>1750.00</td>\n",
       "      <td>1756.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1800.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>1804.50</td>\n",
       "      <td>1809.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>56.000000</td>\n",
       "      <td>29.698485</td>\n",
       "      <td>35.0</td>\n",
       "      <td>45.50</td>\n",
       "      <td>56.0</td>\n",
       "      <td>66.50</td>\n",
       "      <td>77.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Czechia</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1731.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1731.0</td>\n",
       "      <td>1731.00</td>\n",
       "      <td>1731.0</td>\n",
       "      <td>1731.00</td>\n",
       "      <td>1731.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1799.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>1799.00</td>\n",
       "      <td>1799.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>68.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>68.0</td>\n",
       "      <td>68.00</td>\n",
       "      <td>68.0</td>\n",
       "      <td>68.00</td>\n",
       "      <td>68.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Italy</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1749.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1749.0</td>\n",
       "      <td>1749.00</td>\n",
       "      <td>1749.0</td>\n",
       "      <td>1749.00</td>\n",
       "      <td>1749.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1801.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>1801.00</td>\n",
       "      <td>1801.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>52.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>52.0</td>\n",
       "      <td>52.00</td>\n",
       "      <td>52.0</td>\n",
       "      <td>52.00</td>\n",
       "      <td>52.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Spain</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1754.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1754.0</td>\n",
       "      <td>1754.00</td>\n",
       "      <td>1754.0</td>\n",
       "      <td>1754.00</td>\n",
       "      <td>1754.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1806.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>1806.00</td>\n",
       "      <td>1806.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>52.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>52.0</td>\n",
       "      <td>52.00</td>\n",
       "      <td>52.0</td>\n",
       "      <td>52.00</td>\n",
       "      <td>52.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"8\" valign=\"top\">modern</th>\n",
       "      <th>Austria</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1885.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1885.0</td>\n",
       "      <td>1885.00</td>\n",
       "      <td>1885.0</td>\n",
       "      <td>1885.00</td>\n",
       "      <td>1885.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1935.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>1935.00</td>\n",
       "      <td>1935.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>50.0</td>\n",
       "      <td>50.00</td>\n",
       "      <td>50.0</td>\n",
       "      <td>50.00</td>\n",
       "      <td>50.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Czechia</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1854.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1854.0</td>\n",
       "      <td>1854.00</td>\n",
       "      <td>1854.0</td>\n",
       "      <td>1854.00</td>\n",
       "      <td>1854.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1928.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>1928.00</td>\n",
       "      <td>1928.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>74.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>74.0</td>\n",
       "      <td>74.00</td>\n",
       "      <td>74.0</td>\n",
       "      <td>74.00</td>\n",
       "      <td>74.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>England</th>\n",
       "      <td>2.0</td>\n",
       "      <td>1936.500000</td>\n",
       "      <td>48.790368</td>\n",
       "      <td>1902.0</td>\n",
       "      <td>1919.25</td>\n",
       "      <td>1936.5</td>\n",
       "      <td>1953.75</td>\n",
       "      <td>1971.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1983.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>1983.00</td>\n",
       "      <td>1983.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>81.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>81.0</td>\n",
       "      <td>81.00</td>\n",
       "      <td>81.0</td>\n",
       "      <td>81.00</td>\n",
       "      <td>81.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>France</th>\n",
       "      <td>2.0</td>\n",
       "      <td>1916.500000</td>\n",
       "      <td>12.020815</td>\n",
       "      <td>1908.0</td>\n",
       "      <td>1912.25</td>\n",
       "      <td>1916.5</td>\n",
       "      <td>1920.75</td>\n",
       "      <td>1925.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2004.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>2010.00</td>\n",
       "      <td>2016.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>87.500000</td>\n",
       "      <td>4.949747</td>\n",
       "      <td>84.0</td>\n",
       "      <td>85.75</td>\n",
       "      <td>87.5</td>\n",
       "      <td>89.25</td>\n",
       "      <td>91.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Germany</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1895.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1895.0</td>\n",
       "      <td>1895.00</td>\n",
       "      <td>1895.0</td>\n",
       "      <td>1895.00</td>\n",
       "      <td>1895.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1982.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>1982.00</td>\n",
       "      <td>1982.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>87.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>87.0</td>\n",
       "      <td>87.00</td>\n",
       "      <td>87.0</td>\n",
       "      <td>87.00</td>\n",
       "      <td>87.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RUssia</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1891.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1891.0</td>\n",
       "      <td>1891.00</td>\n",
       "      <td>1891.0</td>\n",
       "      <td>1891.00</td>\n",
       "      <td>1891.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1953.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>1953.00</td>\n",
       "      <td>1953.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>62.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>62.0</td>\n",
       "      <td>62.00</td>\n",
       "      <td>62.0</td>\n",
       "      <td>62.00</td>\n",
       "      <td>62.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Russia</th>\n",
       "      <td>2.0</td>\n",
       "      <td>1894.000000</td>\n",
       "      <td>16.970563</td>\n",
       "      <td>1882.0</td>\n",
       "      <td>1888.00</td>\n",
       "      <td>1894.0</td>\n",
       "      <td>1900.00</td>\n",
       "      <td>1906.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1973.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>1974.00</td>\n",
       "      <td>1975.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>79.000000</td>\n",
       "      <td>14.142136</td>\n",
       "      <td>69.0</td>\n",
       "      <td>74.00</td>\n",
       "      <td>79.0</td>\n",
       "      <td>84.00</td>\n",
       "      <td>89.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>USA</th>\n",
       "      <td>3.0</td>\n",
       "      <td>1918.333333</td>\n",
       "      <td>18.502252</td>\n",
       "      <td>1900.0</td>\n",
       "      <td>1909.00</td>\n",
       "      <td>1918.0</td>\n",
       "      <td>1927.50</td>\n",
       "      <td>1937.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1990.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>1990.00</td>\n",
       "      <td>1990.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>81.000000</td>\n",
       "      <td>12.727922</td>\n",
       "      <td>72.0</td>\n",
       "      <td>76.50</td>\n",
       "      <td>81.0</td>\n",
       "      <td>85.50</td>\n",
       "      <td>90.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"4\" valign=\"top\">post-romantic</th>\n",
       "      <th>Austria</th>\n",
       "      <td>2.0</td>\n",
       "      <td>1842.000000</td>\n",
       "      <td>25.455844</td>\n",
       "      <td>1824.0</td>\n",
       "      <td>1833.00</td>\n",
       "      <td>1842.0</td>\n",
       "      <td>1851.00</td>\n",
       "      <td>1860.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1903.500000</td>\n",
       "      <td>...</td>\n",
       "      <td>1907.25</td>\n",
       "      <td>1911.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>61.500000</td>\n",
       "      <td>14.849242</td>\n",
       "      <td>51.0</td>\n",
       "      <td>56.25</td>\n",
       "      <td>61.5</td>\n",
       "      <td>66.75</td>\n",
       "      <td>72.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Finland</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1865.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1865.0</td>\n",
       "      <td>1865.00</td>\n",
       "      <td>1865.0</td>\n",
       "      <td>1865.00</td>\n",
       "      <td>1865.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1957.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>1957.00</td>\n",
       "      <td>1957.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>92.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>92.0</td>\n",
       "      <td>92.00</td>\n",
       "      <td>92.0</td>\n",
       "      <td>92.00</td>\n",
       "      <td>92.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Germany</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1864.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1864.0</td>\n",
       "      <td>1864.00</td>\n",
       "      <td>1864.0</td>\n",
       "      <td>1864.00</td>\n",
       "      <td>1864.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1949.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>1949.00</td>\n",
       "      <td>1949.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>85.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>85.0</td>\n",
       "      <td>85.00</td>\n",
       "      <td>85.0</td>\n",
       "      <td>85.00</td>\n",
       "      <td>85.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Italy</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1858.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1858.0</td>\n",
       "      <td>1858.00</td>\n",
       "      <td>1858.0</td>\n",
       "      <td>1858.00</td>\n",
       "      <td>1858.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1924.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>1924.00</td>\n",
       "      <td>1924.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>66.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>66.0</td>\n",
       "      <td>66.00</td>\n",
       "      <td>66.0</td>\n",
       "      <td>66.00</td>\n",
       "      <td>66.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">renaissance</th>\n",
       "      <th>Belgium</th>\n",
       "      <td>2.0</td>\n",
       "      <td>1464.500000</td>\n",
       "      <td>95.459415</td>\n",
       "      <td>1397.0</td>\n",
       "      <td>1430.75</td>\n",
       "      <td>1464.5</td>\n",
       "      <td>1498.25</td>\n",
       "      <td>1532.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1534.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>1564.00</td>\n",
       "      <td>1594.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>69.500000</td>\n",
       "      <td>10.606602</td>\n",
       "      <td>62.0</td>\n",
       "      <td>65.75</td>\n",
       "      <td>69.5</td>\n",
       "      <td>73.25</td>\n",
       "      <td>77.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>England</th>\n",
       "      <td>2.0</td>\n",
       "      <td>1551.500000</td>\n",
       "      <td>16.263456</td>\n",
       "      <td>1540.0</td>\n",
       "      <td>1545.75</td>\n",
       "      <td>1551.5</td>\n",
       "      <td>1557.25</td>\n",
       "      <td>1563.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1624.500000</td>\n",
       "      <td>...</td>\n",
       "      <td>1625.25</td>\n",
       "      <td>1626.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>73.000000</td>\n",
       "      <td>14.142136</td>\n",
       "      <td>63.0</td>\n",
       "      <td>68.00</td>\n",
       "      <td>73.0</td>\n",
       "      <td>78.00</td>\n",
       "      <td>83.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Italy</th>\n",
       "      <td>3.0</td>\n",
       "      <td>1552.666667</td>\n",
       "      <td>23.965253</td>\n",
       "      <td>1525.0</td>\n",
       "      <td>1545.50</td>\n",
       "      <td>1566.0</td>\n",
       "      <td>1566.50</td>\n",
       "      <td>1567.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1616.666667</td>\n",
       "      <td>...</td>\n",
       "      <td>1628.00</td>\n",
       "      <td>1643.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>64.000000</td>\n",
       "      <td>15.132746</td>\n",
       "      <td>47.0</td>\n",
       "      <td>58.00</td>\n",
       "      <td>69.0</td>\n",
       "      <td>72.50</td>\n",
       "      <td>76.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"6\" valign=\"top\">romantic</th>\n",
       "      <th>Czechia</th>\n",
       "      <td>2.0</td>\n",
       "      <td>1832.500000</td>\n",
       "      <td>12.020815</td>\n",
       "      <td>1824.0</td>\n",
       "      <td>1828.25</td>\n",
       "      <td>1832.5</td>\n",
       "      <td>1836.75</td>\n",
       "      <td>1841.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1894.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>1899.00</td>\n",
       "      <td>1904.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>61.500000</td>\n",
       "      <td>2.121320</td>\n",
       "      <td>60.0</td>\n",
       "      <td>60.75</td>\n",
       "      <td>61.5</td>\n",
       "      <td>62.25</td>\n",
       "      <td>63.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>France</th>\n",
       "      <td>3.0</td>\n",
       "      <td>1821.000000</td>\n",
       "      <td>19.672316</td>\n",
       "      <td>1803.0</td>\n",
       "      <td>1810.50</td>\n",
       "      <td>1818.0</td>\n",
       "      <td>1830.00</td>\n",
       "      <td>1842.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1891.333333</td>\n",
       "      <td>...</td>\n",
       "      <td>1902.50</td>\n",
       "      <td>1912.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>70.333333</td>\n",
       "      <td>4.509250</td>\n",
       "      <td>66.0</td>\n",
       "      <td>68.00</td>\n",
       "      <td>70.0</td>\n",
       "      <td>72.50</td>\n",
       "      <td>75.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Germany</th>\n",
       "      <td>4.0</td>\n",
       "      <td>1806.500000</td>\n",
       "      <td>26.388129</td>\n",
       "      <td>1770.0</td>\n",
       "      <td>1800.00</td>\n",
       "      <td>1811.5</td>\n",
       "      <td>1818.00</td>\n",
       "      <td>1833.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1865.750000</td>\n",
       "      <td>...</td>\n",
       "      <td>1886.50</td>\n",
       "      <td>1897.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>59.250000</td>\n",
       "      <td>10.307764</td>\n",
       "      <td>46.0</td>\n",
       "      <td>54.25</td>\n",
       "      <td>60.5</td>\n",
       "      <td>65.50</td>\n",
       "      <td>70.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Italy</th>\n",
       "      <td>4.0</td>\n",
       "      <td>1817.250000</td>\n",
       "      <td>28.004464</td>\n",
       "      <td>1797.0</td>\n",
       "      <td>1800.00</td>\n",
       "      <td>1807.0</td>\n",
       "      <td>1824.25</td>\n",
       "      <td>1858.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1875.750000</td>\n",
       "      <td>...</td>\n",
       "      <td>1905.50</td>\n",
       "      <td>1919.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>58.500000</td>\n",
       "      <td>22.605309</td>\n",
       "      <td>34.0</td>\n",
       "      <td>46.75</td>\n",
       "      <td>56.0</td>\n",
       "      <td>67.75</td>\n",
       "      <td>88.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Russia</th>\n",
       "      <td>2.0</td>\n",
       "      <td>1836.000000</td>\n",
       "      <td>4.242641</td>\n",
       "      <td>1833.0</td>\n",
       "      <td>1834.50</td>\n",
       "      <td>1836.0</td>\n",
       "      <td>1837.50</td>\n",
       "      <td>1839.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1884.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>1885.50</td>\n",
       "      <td>1887.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>48.000000</td>\n",
       "      <td>8.485281</td>\n",
       "      <td>42.0</td>\n",
       "      <td>45.00</td>\n",
       "      <td>48.0</td>\n",
       "      <td>51.00</td>\n",
       "      <td>54.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Spain</th>\n",
       "      <td>2.0</td>\n",
       "      <td>1863.500000</td>\n",
       "      <td>4.949747</td>\n",
       "      <td>1860.0</td>\n",
       "      <td>1861.75</td>\n",
       "      <td>1863.5</td>\n",
       "      <td>1865.25</td>\n",
       "      <td>1867.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1912.500000</td>\n",
       "      <td>...</td>\n",
       "      <td>1914.25</td>\n",
       "      <td>1916.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>49.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>49.0</td>\n",
       "      <td>49.00</td>\n",
       "      <td>49.0</td>\n",
       "      <td>49.00</td>\n",
       "      <td>49.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>29 rows × 24 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                      birth                                                   \\\n",
       "                      count         mean        std     min      25%     50%   \n",
       "period        country                                                          \n",
       "baroque       England   1.0  1659.000000        NaN  1659.0  1659.00  1659.0   \n",
       "              France    3.0  1650.666667  29.263174  1626.0  1634.50  1643.0   \n",
       "              Germany   2.0  1685.000000   0.000000  1685.0  1685.00  1685.0   \n",
       "              Italy     4.0  1663.000000  53.285395  1587.0  1649.25  1677.5   \n",
       "classic       Austria   2.0  1744.000000  16.970563  1732.0  1738.00  1744.0   \n",
       "              Czechia   1.0  1731.000000        NaN  1731.0  1731.00  1731.0   \n",
       "              Italy     1.0  1749.000000        NaN  1749.0  1749.00  1749.0   \n",
       "              Spain     1.0  1754.000000        NaN  1754.0  1754.00  1754.0   \n",
       "modern        Austria   1.0  1885.000000        NaN  1885.0  1885.00  1885.0   \n",
       "              Czechia   1.0  1854.000000        NaN  1854.0  1854.00  1854.0   \n",
       "              England   2.0  1936.500000  48.790368  1902.0  1919.25  1936.5   \n",
       "              France    2.0  1916.500000  12.020815  1908.0  1912.25  1916.5   \n",
       "              Germany   1.0  1895.000000        NaN  1895.0  1895.00  1895.0   \n",
       "              RUssia    1.0  1891.000000        NaN  1891.0  1891.00  1891.0   \n",
       "              Russia    2.0  1894.000000  16.970563  1882.0  1888.00  1894.0   \n",
       "              USA       3.0  1918.333333  18.502252  1900.0  1909.00  1918.0   \n",
       "post-romantic Austria   2.0  1842.000000  25.455844  1824.0  1833.00  1842.0   \n",
       "              Finland   1.0  1865.000000        NaN  1865.0  1865.00  1865.0   \n",
       "              Germany   1.0  1864.000000        NaN  1864.0  1864.00  1864.0   \n",
       "              Italy     1.0  1858.000000        NaN  1858.0  1858.00  1858.0   \n",
       "renaissance   Belgium   2.0  1464.500000  95.459415  1397.0  1430.75  1464.5   \n",
       "              England   2.0  1551.500000  16.263456  1540.0  1545.75  1551.5   \n",
       "              Italy     3.0  1552.666667  23.965253  1525.0  1545.50  1566.0   \n",
       "romantic      Czechia   2.0  1832.500000  12.020815  1824.0  1828.25  1832.5   \n",
       "              France    3.0  1821.000000  19.672316  1803.0  1810.50  1818.0   \n",
       "              Germany   4.0  1806.500000  26.388129  1770.0  1800.00  1811.5   \n",
       "              Italy     4.0  1817.250000  28.004464  1797.0  1800.00  1807.0   \n",
       "              Russia    2.0  1836.000000   4.242641  1833.0  1834.50  1836.0   \n",
       "              Spain     2.0  1863.500000   4.949747  1860.0  1861.75  1863.5   \n",
       "\n",
       "                                       death               ...           \\\n",
       "                           75%     max count         mean  ...      75%   \n",
       "period        country                                      ...            \n",
       "baroque       England  1659.00  1659.0   1.0  1695.000000  ...  1695.00   \n",
       "              France   1663.00  1683.0   3.0  1709.666667  ...  1734.00   \n",
       "              Germany  1685.00  1685.0   2.0  1754.500000  ...  1756.75   \n",
       "              Italy    1691.25  1710.0   4.0  1717.250000  ...  1741.25   \n",
       "classic       Austria  1750.00  1756.0   2.0  1800.000000  ...  1804.50   \n",
       "              Czechia  1731.00  1731.0   1.0  1799.000000  ...  1799.00   \n",
       "              Italy    1749.00  1749.0   1.0  1801.000000  ...  1801.00   \n",
       "              Spain    1754.00  1754.0   1.0  1806.000000  ...  1806.00   \n",
       "modern        Austria  1885.00  1885.0   1.0  1935.000000  ...  1935.00   \n",
       "              Czechia  1854.00  1854.0   1.0  1928.000000  ...  1928.00   \n",
       "              England  1953.75  1971.0   1.0  1983.000000  ...  1983.00   \n",
       "              France   1920.75  1925.0   2.0  2004.000000  ...  2010.00   \n",
       "              Germany  1895.00  1895.0   1.0  1982.000000  ...  1982.00   \n",
       "              RUssia   1891.00  1891.0   1.0  1953.000000  ...  1953.00   \n",
       "              Russia   1900.00  1906.0   2.0  1973.000000  ...  1974.00   \n",
       "              USA      1927.50  1937.0   2.0  1990.000000  ...  1990.00   \n",
       "post-romantic Austria  1851.00  1860.0   2.0  1903.500000  ...  1907.25   \n",
       "              Finland  1865.00  1865.0   1.0  1957.000000  ...  1957.00   \n",
       "              Germany  1864.00  1864.0   1.0  1949.000000  ...  1949.00   \n",
       "              Italy    1858.00  1858.0   1.0  1924.000000  ...  1924.00   \n",
       "renaissance   Belgium  1498.25  1532.0   2.0  1534.000000  ...  1564.00   \n",
       "              England  1557.25  1563.0   2.0  1624.500000  ...  1625.25   \n",
       "              Italy    1566.50  1567.0   3.0  1616.666667  ...  1628.00   \n",
       "romantic      Czechia  1836.75  1841.0   2.0  1894.000000  ...  1899.00   \n",
       "              France   1830.00  1842.0   3.0  1891.333333  ...  1902.50   \n",
       "              Germany  1818.00  1833.0   4.0  1865.750000  ...  1886.50   \n",
       "              Italy    1824.25  1858.0   4.0  1875.750000  ...  1905.50   \n",
       "              Russia   1837.50  1839.0   2.0  1884.000000  ...  1885.50   \n",
       "              Spain    1865.25  1867.0   2.0  1912.500000  ...  1914.25   \n",
       "\n",
       "                                age                                           \\\n",
       "                          max count       mean        std   min    25%   50%   \n",
       "period        country                                                          \n",
       "baroque       England  1695.0   1.0  36.000000        NaN  36.0  36.00  36.0   \n",
       "              France   1764.0   3.0  59.000000  23.065125  35.0  48.00  61.0   \n",
       "              Germany  1759.0   2.0  69.500000   6.363961  65.0  67.25  69.5   \n",
       "              Italy    1757.0   4.0  54.250000  20.434856  26.0  46.25  59.5   \n",
       "classic       Austria  1809.0   2.0  56.000000  29.698485  35.0  45.50  56.0   \n",
       "              Czechia  1799.0   1.0  68.000000        NaN  68.0  68.00  68.0   \n",
       "              Italy    1801.0   1.0  52.000000        NaN  52.0  52.00  52.0   \n",
       "              Spain    1806.0   1.0  52.000000        NaN  52.0  52.00  52.0   \n",
       "modern        Austria  1935.0   1.0  50.000000        NaN  50.0  50.00  50.0   \n",
       "              Czechia  1928.0   1.0  74.000000        NaN  74.0  74.00  74.0   \n",
       "              England  1983.0   1.0  81.000000        NaN  81.0  81.00  81.0   \n",
       "              France   2016.0   2.0  87.500000   4.949747  84.0  85.75  87.5   \n",
       "              Germany  1982.0   1.0  87.000000        NaN  87.0  87.00  87.0   \n",
       "              RUssia   1953.0   1.0  62.000000        NaN  62.0  62.00  62.0   \n",
       "              Russia   1975.0   2.0  79.000000  14.142136  69.0  74.00  79.0   \n",
       "              USA      1990.0   2.0  81.000000  12.727922  72.0  76.50  81.0   \n",
       "post-romantic Austria  1911.0   2.0  61.500000  14.849242  51.0  56.25  61.5   \n",
       "              Finland  1957.0   1.0  92.000000        NaN  92.0  92.00  92.0   \n",
       "              Germany  1949.0   1.0  85.000000        NaN  85.0  85.00  85.0   \n",
       "              Italy    1924.0   1.0  66.000000        NaN  66.0  66.00  66.0   \n",
       "renaissance   Belgium  1594.0   2.0  69.500000  10.606602  62.0  65.75  69.5   \n",
       "              England  1626.0   2.0  73.000000  14.142136  63.0  68.00  73.0   \n",
       "              Italy    1643.0   3.0  64.000000  15.132746  47.0  58.00  69.0   \n",
       "romantic      Czechia  1904.0   2.0  61.500000   2.121320  60.0  60.75  61.5   \n",
       "              France   1912.0   3.0  70.333333   4.509250  66.0  68.00  70.0   \n",
       "              Germany  1897.0   4.0  59.250000  10.307764  46.0  54.25  60.5   \n",
       "              Italy    1919.0   4.0  58.500000  22.605309  34.0  46.75  56.0   \n",
       "              Russia   1887.0   2.0  48.000000   8.485281  42.0  45.00  48.0   \n",
       "              Spain    1916.0   2.0  49.000000   0.000000  49.0  49.00  49.0   \n",
       "\n",
       "                                    \n",
       "                         75%   max  \n",
       "period        country               \n",
       "baroque       England  36.00  36.0  \n",
       "              France   71.00  81.0  \n",
       "              Germany  71.75  74.0  \n",
       "              Italy    67.50  72.0  \n",
       "classic       Austria  66.50  77.0  \n",
       "              Czechia  68.00  68.0  \n",
       "              Italy    52.00  52.0  \n",
       "              Spain    52.00  52.0  \n",
       "modern        Austria  50.00  50.0  \n",
       "              Czechia  74.00  74.0  \n",
       "              England  81.00  81.0  \n",
       "              France   89.25  91.0  \n",
       "              Germany  87.00  87.0  \n",
       "              RUssia   62.00  62.0  \n",
       "              Russia   84.00  89.0  \n",
       "              USA      85.50  90.0  \n",
       "post-romantic Austria  66.75  72.0  \n",
       "              Finland  92.00  92.0  \n",
       "              Germany  85.00  85.0  \n",
       "              Italy    66.00  66.0  \n",
       "renaissance   Belgium  73.25  77.0  \n",
       "              England  78.00  83.0  \n",
       "              Italy    72.50  76.0  \n",
       "romantic      Czechia  62.25  63.0  \n",
       "              France   72.50  75.0  \n",
       "              Germany  65.50  70.0  \n",
       "              Italy    67.75  88.0  \n",
       "              Russia   51.00  54.0  \n",
       "              Spain    49.00  49.0  \n",
       "\n",
       "[29 rows x 24 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "composer_grouped = composers.groupby(['period','country'])\n",
    "composer_grouped.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>composer</th>\n",
       "      <th>birth</th>\n",
       "      <th>death</th>\n",
       "      <th>period</th>\n",
       "      <th>country</th>\n",
       "      <th>age</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>Haendel</td>\n",
       "      <td>1685</td>\n",
       "      <td>1759.0</td>\n",
       "      <td>baroque</td>\n",
       "      <td>Germany</td>\n",
       "      <td>74.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>Bach</td>\n",
       "      <td>1685</td>\n",
       "      <td>1750.0</td>\n",
       "      <td>baroque</td>\n",
       "      <td>Germany</td>\n",
       "      <td>65.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   composer  birth   death   period  country   age\n",
       "14  Haendel   1685  1759.0  baroque  Germany  74.0\n",
       "47     Bach   1685  1750.0  baroque  Germany  65.0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "composer_grouped.get_group(('baroque','Germany'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 11.2 Operations on groups"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The main advantage of this Group object is that it allows us to do very quickly both computations and plotting without having to loop through different categories. Indeed Pandas makes all the work for us: it applies functions on each group and then reassembles the results into a Dataframe (or Series depending on the operation).\n",
    "\n",
    "For example we can apply most functions we used for Dataframes (mean, sum etc.) on groups as well and Pandas seamlessly does the work for us:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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></th>\n",
       "      <th>birth</th>\n",
       "      <th>death</th>\n",
       "      <th>age</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>period</th>\n",
       "      <th>country</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"4\" valign=\"top\">baroque</th>\n",
       "      <th>England</th>\n",
       "      <td>1659.000000</td>\n",
       "      <td>1695.000000</td>\n",
       "      <td>36.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>France</th>\n",
       "      <td>1650.666667</td>\n",
       "      <td>1709.666667</td>\n",
       "      <td>59.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Germany</th>\n",
       "      <td>1685.000000</td>\n",
       "      <td>1754.500000</td>\n",
       "      <td>69.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Italy</th>\n",
       "      <td>1663.000000</td>\n",
       "      <td>1717.250000</td>\n",
       "      <td>54.250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"4\" valign=\"top\">classic</th>\n",
       "      <th>Austria</th>\n",
       "      <td>1744.000000</td>\n",
       "      <td>1800.000000</td>\n",
       "      <td>56.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Czechia</th>\n",
       "      <td>1731.000000</td>\n",
       "      <td>1799.000000</td>\n",
       "      <td>68.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Italy</th>\n",
       "      <td>1749.000000</td>\n",
       "      <td>1801.000000</td>\n",
       "      <td>52.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Spain</th>\n",
       "      <td>1754.000000</td>\n",
       "      <td>1806.000000</td>\n",
       "      <td>52.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"8\" valign=\"top\">modern</th>\n",
       "      <th>Austria</th>\n",
       "      <td>1885.000000</td>\n",
       "      <td>1935.000000</td>\n",
       "      <td>50.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Czechia</th>\n",
       "      <td>1854.000000</td>\n",
       "      <td>1928.000000</td>\n",
       "      <td>74.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>England</th>\n",
       "      <td>1936.500000</td>\n",
       "      <td>1983.000000</td>\n",
       "      <td>81.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>France</th>\n",
       "      <td>1916.500000</td>\n",
       "      <td>2004.000000</td>\n",
       "      <td>87.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Germany</th>\n",
       "      <td>1895.000000</td>\n",
       "      <td>1982.000000</td>\n",
       "      <td>87.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RUssia</th>\n",
       "      <td>1891.000000</td>\n",
       "      <td>1953.000000</td>\n",
       "      <td>62.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Russia</th>\n",
       "      <td>1894.000000</td>\n",
       "      <td>1973.000000</td>\n",
       "      <td>79.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>USA</th>\n",
       "      <td>1918.333333</td>\n",
       "      <td>1990.000000</td>\n",
       "      <td>81.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"4\" valign=\"top\">post-romantic</th>\n",
       "      <th>Austria</th>\n",
       "      <td>1842.000000</td>\n",
       "      <td>1903.500000</td>\n",
       "      <td>61.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Finland</th>\n",
       "      <td>1865.000000</td>\n",
       "      <td>1957.000000</td>\n",
       "      <td>92.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Germany</th>\n",
       "      <td>1864.000000</td>\n",
       "      <td>1949.000000</td>\n",
       "      <td>85.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Italy</th>\n",
       "      <td>1858.000000</td>\n",
       "      <td>1924.000000</td>\n",
       "      <td>66.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">renaissance</th>\n",
       "      <th>Belgium</th>\n",
       "      <td>1464.500000</td>\n",
       "      <td>1534.000000</td>\n",
       "      <td>69.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>England</th>\n",
       "      <td>1551.500000</td>\n",
       "      <td>1624.500000</td>\n",
       "      <td>73.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Italy</th>\n",
       "      <td>1552.666667</td>\n",
       "      <td>1616.666667</td>\n",
       "      <td>64.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"6\" valign=\"top\">romantic</th>\n",
       "      <th>Czechia</th>\n",
       "      <td>1832.500000</td>\n",
       "      <td>1894.000000</td>\n",
       "      <td>61.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>France</th>\n",
       "      <td>1821.000000</td>\n",
       "      <td>1891.333333</td>\n",
       "      <td>70.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Germany</th>\n",
       "      <td>1806.500000</td>\n",
       "      <td>1865.750000</td>\n",
       "      <td>59.250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Italy</th>\n",
       "      <td>1817.250000</td>\n",
       "      <td>1875.750000</td>\n",
       "      <td>58.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Russia</th>\n",
       "      <td>1836.000000</td>\n",
       "      <td>1884.000000</td>\n",
       "      <td>48.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Spain</th>\n",
       "      <td>1863.500000</td>\n",
       "      <td>1912.500000</td>\n",
       "      <td>49.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                             birth        death        age\n",
       "period        country                                     \n",
       "baroque       England  1659.000000  1695.000000  36.000000\n",
       "              France   1650.666667  1709.666667  59.000000\n",
       "              Germany  1685.000000  1754.500000  69.500000\n",
       "              Italy    1663.000000  1717.250000  54.250000\n",
       "classic       Austria  1744.000000  1800.000000  56.000000\n",
       "              Czechia  1731.000000  1799.000000  68.000000\n",
       "              Italy    1749.000000  1801.000000  52.000000\n",
       "              Spain    1754.000000  1806.000000  52.000000\n",
       "modern        Austria  1885.000000  1935.000000  50.000000\n",
       "              Czechia  1854.000000  1928.000000  74.000000\n",
       "              England  1936.500000  1983.000000  81.000000\n",
       "              France   1916.500000  2004.000000  87.500000\n",
       "              Germany  1895.000000  1982.000000  87.000000\n",
       "              RUssia   1891.000000  1953.000000  62.000000\n",
       "              Russia   1894.000000  1973.000000  79.000000\n",
       "              USA      1918.333333  1990.000000  81.000000\n",
       "post-romantic Austria  1842.000000  1903.500000  61.500000\n",
       "              Finland  1865.000000  1957.000000  92.000000\n",
       "              Germany  1864.000000  1949.000000  85.000000\n",
       "              Italy    1858.000000  1924.000000  66.000000\n",
       "renaissance   Belgium  1464.500000  1534.000000  69.500000\n",
       "              England  1551.500000  1624.500000  73.000000\n",
       "              Italy    1552.666667  1616.666667  64.000000\n",
       "romantic      Czechia  1832.500000  1894.000000  61.500000\n",
       "              France   1821.000000  1891.333333  70.333333\n",
       "              Germany  1806.500000  1865.750000  59.250000\n",
       "              Italy    1817.250000  1875.750000  58.500000\n",
       "              Russia   1836.000000  1884.000000  48.000000\n",
       "              Spain    1863.500000  1912.500000  49.000000"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "composer_grouped.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th rowspan=\"4\" valign=\"top\">baroque</th>\n",
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       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
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       "      <th>Germany</th>\n",
       "      <td>2</td>\n",
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       "      <th>Italy</th>\n",
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       "      <td>4</td>\n",
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       "      <th rowspan=\"4\" valign=\"top\">classic</th>\n",
       "      <th>Austria</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
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       "      <th>Czechia</th>\n",
       "      <td>1</td>\n",
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       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Italy</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Spain</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"8\" valign=\"top\">modern</th>\n",
       "      <th>Austria</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Czechia</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>England</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>France</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Germany</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RUssia</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Russia</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>USA</th>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"4\" valign=\"top\">post-romantic</th>\n",
       "      <th>Austria</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Finland</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Germany</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Italy</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">renaissance</th>\n",
       "      <th>Belgium</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>England</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Italy</th>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"6\" valign=\"top\">romantic</th>\n",
       "      <th>Czechia</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>France</th>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Germany</th>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Italy</th>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Russia</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Spain</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       composer  birth  death  age\n",
       "period        country                             \n",
       "baroque       England         1      1      1    1\n",
       "              France          3      3      3    3\n",
       "              Germany         2      2      2    2\n",
       "              Italy           4      4      4    4\n",
       "classic       Austria         2      2      2    2\n",
       "              Czechia         1      1      1    1\n",
       "              Italy           1      1      1    1\n",
       "              Spain           1      1      1    1\n",
       "modern        Austria         1      1      1    1\n",
       "              Czechia         1      1      1    1\n",
       "              England         2      2      1    1\n",
       "              France          2      2      2    2\n",
       "              Germany         1      1      1    1\n",
       "              RUssia          1      1      1    1\n",
       "              Russia          2      2      2    2\n",
       "              USA             3      3      2    2\n",
       "post-romantic Austria         2      2      2    2\n",
       "              Finland         1      1      1    1\n",
       "              Germany         1      1      1    1\n",
       "              Italy           1      1      1    1\n",
       "renaissance   Belgium         2      2      2    2\n",
       "              England         2      2      2    2\n",
       "              Italy           3      3      3    3\n",
       "romantic      Czechia         2      2      2    2\n",
       "              France          3      3      3    3\n",
       "              Germany         4      4      4    4\n",
       "              Italy           4      4      4    4\n",
       "              Russia          2      2      2    2\n",
       "              Spain           2      2      2    2"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "composer_grouped.count()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also design specific functions (again, like in the case of Dataframes) and apply them on groups:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mult(myseries):\n",
    "    return myseries.max() * 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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>composer</th>\n",
       "      <th>birth</th>\n",
       "      <th>death</th>\n",
       "      <th>period</th>\n",
       "      <th>country</th>\n",
       "      <th>age</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>period</th>\n",
       "      <th>country</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=\"4\" valign=\"top\">baroque</th>\n",
       "      <th>England</th>\n",
       "      <td>PurcellPurcellPurcell</td>\n",
       "      <td>4977</td>\n",
       "      <td>5085.0</td>\n",
       "      <td>baroquebaroquebaroque</td>\n",
       "      <td>EnglandEnglandEngland</td>\n",
       "      <td>108.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>France</th>\n",
       "      <td>RameauRameauRameau</td>\n",
       "      <td>5049</td>\n",
       "      <td>5292.0</td>\n",
       "      <td>baroquebaroquebaroque</td>\n",
       "      <td>FranceFranceFrance</td>\n",
       "      <td>243.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Germany</th>\n",
       "      <td>HaendelHaendelHaendel</td>\n",
       "      <td>5055</td>\n",
       "      <td>5277.0</td>\n",
       "      <td>baroquebaroquebaroque</td>\n",
       "      <td>GermanyGermanyGermany</td>\n",
       "      <td>222.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Italy</th>\n",
       "      <td>ScarlattiScarlattiScarlatti</td>\n",
       "      <td>5130</td>\n",
       "      <td>5271.0</td>\n",
       "      <td>baroquebaroquebaroque</td>\n",
       "      <td>ItalyItalyItaly</td>\n",
       "      <td>216.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"4\" valign=\"top\">classic</th>\n",
       "      <th>Austria</th>\n",
       "      <td>MozartMozartMozart</td>\n",
       "      <td>5268</td>\n",
       "      <td>5427.0</td>\n",
       "      <td>classicclassicclassic</td>\n",
       "      <td>AustriaAustriaAustria</td>\n",
       "      <td>231.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Czechia</th>\n",
       "      <td>DusekDusekDusek</td>\n",
       "      <td>5193</td>\n",
       "      <td>5397.0</td>\n",
       "      <td>classicclassicclassic</td>\n",
       "      <td>CzechiaCzechiaCzechia</td>\n",
       "      <td>204.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Italy</th>\n",
       "      <td>CimarosaCimarosaCimarosa</td>\n",
       "      <td>5247</td>\n",
       "      <td>5403.0</td>\n",
       "      <td>classicclassicclassic</td>\n",
       "      <td>ItalyItalyItaly</td>\n",
       "      <td>156.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Spain</th>\n",
       "      <td>SolerSolerSoler</td>\n",
       "      <td>5262</td>\n",
       "      <td>5418.0</td>\n",
       "      <td>classicclassicclassic</td>\n",
       "      <td>SpainSpainSpain</td>\n",
       "      <td>156.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"8\" valign=\"top\">modern</th>\n",
       "      <th>Austria</th>\n",
       "      <td>BergBergBerg</td>\n",
       "      <td>5655</td>\n",
       "      <td>5805.0</td>\n",
       "      <td>modernmodernmodern</td>\n",
       "      <td>AustriaAustriaAustria</td>\n",
       "      <td>150.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Czechia</th>\n",
       "      <td>JanacekJanacekJanacek</td>\n",
       "      <td>5562</td>\n",
       "      <td>5784.0</td>\n",
       "      <td>modernmodernmodern</td>\n",
       "      <td>CzechiaCzechiaCzechia</td>\n",
       "      <td>222.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>England</th>\n",
       "      <td>WaltonWaltonWalton</td>\n",
       "      <td>5913</td>\n",
       "      <td>5949.0</td>\n",
       "      <td>modernmodernmodern</td>\n",
       "      <td>EnglandEnglandEngland</td>\n",
       "      <td>243.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>France</th>\n",
       "      <td>MessiaenMessiaenMessiaen</td>\n",
       "      <td>5775</td>\n",
       "      <td>6048.0</td>\n",
       "      <td>modernmodernmodern</td>\n",
       "      <td>FranceFranceFrance</td>\n",
       "      <td>273.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Germany</th>\n",
       "      <td>OrffOrffOrff</td>\n",
       "      <td>5685</td>\n",
       "      <td>5946.0</td>\n",
       "      <td>modernmodernmodern</td>\n",
       "      <td>GermanyGermanyGermany</td>\n",
       "      <td>261.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RUssia</th>\n",
       "      <td>ProkofievProkofievProkofiev</td>\n",
       "      <td>5673</td>\n",
       "      <td>5859.0</td>\n",
       "      <td>modernmodernmodern</td>\n",
       "      <td>RUssiaRUssiaRUssia</td>\n",
       "      <td>186.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Russia</th>\n",
       "      <td>StravinskyStravinskyStravinsky</td>\n",
       "      <td>5718</td>\n",
       "      <td>5925.0</td>\n",
       "      <td>modernmodernmodern</td>\n",
       "      <td>RussiaRussiaRussia</td>\n",
       "      <td>267.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>USA</th>\n",
       "      <td>GlassGlassGlass</td>\n",
       "      <td>5811</td>\n",
       "      <td>5970.0</td>\n",
       "      <td>modernmodernmodern</td>\n",
       "      <td>USAUSAUSA</td>\n",
       "      <td>270.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"4\" valign=\"top\">post-romantic</th>\n",
       "      <th>Austria</th>\n",
       "      <td>MahlerMahlerMahler</td>\n",
       "      <td>5580</td>\n",
       "      <td>5733.0</td>\n",
       "      <td>post-romanticpost-romanticpost-romantic</td>\n",
       "      <td>AustriaAustriaAustria</td>\n",
       "      <td>216.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Finland</th>\n",
       "      <td>SibeliusSibeliusSibelius</td>\n",
       "      <td>5595</td>\n",
       "      <td>5871.0</td>\n",
       "      <td>post-romanticpost-romanticpost-romantic</td>\n",
       "      <td>FinlandFinlandFinland</td>\n",
       "      <td>276.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Germany</th>\n",
       "      <td>StraussStraussStrauss</td>\n",
       "      <td>5592</td>\n",
       "      <td>5847.0</td>\n",
       "      <td>post-romanticpost-romanticpost-romantic</td>\n",
       "      <td>GermanyGermanyGermany</td>\n",
       "      <td>255.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Italy</th>\n",
       "      <td>PucciniPucciniPuccini</td>\n",
       "      <td>5574</td>\n",
       "      <td>5772.0</td>\n",
       "      <td>post-romanticpost-romanticpost-romantic</td>\n",
       "      <td>ItalyItalyItaly</td>\n",
       "      <td>198.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">renaissance</th>\n",
       "      <th>Belgium</th>\n",
       "      <td>LassusLassusLassus</td>\n",
       "      <td>4596</td>\n",
       "      <td>4782.0</td>\n",
       "      <td>renaissancerenaissancerenaissance</td>\n",
       "      <td>BelgiumBelgiumBelgium</td>\n",
       "      <td>231.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>England</th>\n",
       "      <td>DowlandDowlandDowland</td>\n",
       "      <td>4689</td>\n",
       "      <td>4878.0</td>\n",
       "      <td>renaissancerenaissancerenaissance</td>\n",
       "      <td>EnglandEnglandEngland</td>\n",
       "      <td>249.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Italy</th>\n",
       "      <td>PalestrinaPalestrinaPalestrina</td>\n",
       "      <td>4701</td>\n",
       "      <td>4929.0</td>\n",
       "      <td>renaissancerenaissancerenaissance</td>\n",
       "      <td>ItalyItalyItaly</td>\n",
       "      <td>228.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"6\" valign=\"top\">romantic</th>\n",
       "      <th>Czechia</th>\n",
       "      <td>SmetanaSmetanaSmetana</td>\n",
       "      <td>5523</td>\n",
       "      <td>5712.0</td>\n",
       "      <td>romanticromanticromantic</td>\n",
       "      <td>CzechiaCzechiaCzechia</td>\n",
       "      <td>189.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>France</th>\n",
       "      <td>MassenetMassenetMassenet</td>\n",
       "      <td>5526</td>\n",
       "      <td>5736.0</td>\n",
       "      <td>romanticromanticromantic</td>\n",
       "      <td>FranceFranceFrance</td>\n",
       "      <td>225.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Germany</th>\n",
       "      <td>WagnerWagnerWagner</td>\n",
       "      <td>5499</td>\n",
       "      <td>5691.0</td>\n",
       "      <td>romanticromanticromantic</td>\n",
       "      <td>GermanyGermanyGermany</td>\n",
       "      <td>210.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Italy</th>\n",
       "      <td>VerdiVerdiVerdi</td>\n",
       "      <td>5574</td>\n",
       "      <td>5757.0</td>\n",
       "      <td>romanticromanticromantic</td>\n",
       "      <td>ItalyItalyItaly</td>\n",
       "      <td>264.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Russia</th>\n",
       "      <td>MussorsgskyMussorsgskyMussorsgsky</td>\n",
       "      <td>5517</td>\n",
       "      <td>5661.0</td>\n",
       "      <td>romanticromanticromantic</td>\n",
       "      <td>RussiaRussiaRussia</td>\n",
       "      <td>162.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Spain</th>\n",
       "      <td>GranadosGranadosGranados</td>\n",
       "      <td>5601</td>\n",
       "      <td>5748.0</td>\n",
       "      <td>romanticromanticromantic</td>\n",
       "      <td>SpainSpainSpain</td>\n",
       "      <td>147.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                composer  birth   death  \\\n",
       "period        country                                                     \n",
       "baroque       England              PurcellPurcellPurcell   4977  5085.0   \n",
       "              France                  RameauRameauRameau   5049  5292.0   \n",
       "              Germany              HaendelHaendelHaendel   5055  5277.0   \n",
       "              Italy          ScarlattiScarlattiScarlatti   5130  5271.0   \n",
       "classic       Austria                 MozartMozartMozart   5268  5427.0   \n",
       "              Czechia                    DusekDusekDusek   5193  5397.0   \n",
       "              Italy             CimarosaCimarosaCimarosa   5247  5403.0   \n",
       "              Spain                      SolerSolerSoler   5262  5418.0   \n",
       "modern        Austria                       BergBergBerg   5655  5805.0   \n",
       "              Czechia              JanacekJanacekJanacek   5562  5784.0   \n",
       "              England                 WaltonWaltonWalton   5913  5949.0   \n",
       "              France            MessiaenMessiaenMessiaen   5775  6048.0   \n",
       "              Germany                       OrffOrffOrff   5685  5946.0   \n",
       "              RUssia         ProkofievProkofievProkofiev   5673  5859.0   \n",
       "              Russia      StravinskyStravinskyStravinsky   5718  5925.0   \n",
       "              USA                        GlassGlassGlass   5811  5970.0   \n",
       "post-romantic Austria                 MahlerMahlerMahler   5580  5733.0   \n",
       "              Finland           SibeliusSibeliusSibelius   5595  5871.0   \n",
       "              Germany              StraussStraussStrauss   5592  5847.0   \n",
       "              Italy                PucciniPucciniPuccini   5574  5772.0   \n",
       "renaissance   Belgium                 LassusLassusLassus   4596  4782.0   \n",
       "              England              DowlandDowlandDowland   4689  4878.0   \n",
       "              Italy       PalestrinaPalestrinaPalestrina   4701  4929.0   \n",
       "romantic      Czechia              SmetanaSmetanaSmetana   5523  5712.0   \n",
       "              France            MassenetMassenetMassenet   5526  5736.0   \n",
       "              Germany                 WagnerWagnerWagner   5499  5691.0   \n",
       "              Italy                      VerdiVerdiVerdi   5574  5757.0   \n",
       "              Russia   MussorsgskyMussorsgskyMussorsgsky   5517  5661.0   \n",
       "              Spain             GranadosGranadosGranados   5601  5748.0   \n",
       "\n",
       "                                                        period  \\\n",
       "period        country                                            \n",
       "baroque       England                    baroquebaroquebaroque   \n",
       "              France                     baroquebaroquebaroque   \n",
       "              Germany                    baroquebaroquebaroque   \n",
       "              Italy                      baroquebaroquebaroque   \n",
       "classic       Austria                    classicclassicclassic   \n",
       "              Czechia                    classicclassicclassic   \n",
       "              Italy                      classicclassicclassic   \n",
       "              Spain                      classicclassicclassic   \n",
       "modern        Austria                       modernmodernmodern   \n",
       "              Czechia                       modernmodernmodern   \n",
       "              England                       modernmodernmodern   \n",
       "              France                        modernmodernmodern   \n",
       "              Germany                       modernmodernmodern   \n",
       "              RUssia                        modernmodernmodern   \n",
       "              Russia                        modernmodernmodern   \n",
       "              USA                           modernmodernmodern   \n",
       "post-romantic Austria  post-romanticpost-romanticpost-romantic   \n",
       "              Finland  post-romanticpost-romanticpost-romantic   \n",
       "              Germany  post-romanticpost-romanticpost-romantic   \n",
       "              Italy    post-romanticpost-romanticpost-romantic   \n",
       "renaissance   Belgium        renaissancerenaissancerenaissance   \n",
       "              England        renaissancerenaissancerenaissance   \n",
       "              Italy          renaissancerenaissancerenaissance   \n",
       "romantic      Czechia                 romanticromanticromantic   \n",
       "              France                  romanticromanticromantic   \n",
       "              Germany                 romanticromanticromantic   \n",
       "              Italy                   romanticromanticromantic   \n",
       "              Russia                  romanticromanticromantic   \n",
       "              Spain                   romanticromanticromantic   \n",
       "\n",
       "                                     country    age  \n",
       "period        country                                \n",
       "baroque       England  EnglandEnglandEngland  108.0  \n",
       "              France      FranceFranceFrance  243.0  \n",
       "              Germany  GermanyGermanyGermany  222.0  \n",
       "              Italy          ItalyItalyItaly  216.0  \n",
       "classic       Austria  AustriaAustriaAustria  231.0  \n",
       "              Czechia  CzechiaCzechiaCzechia  204.0  \n",
       "              Italy          ItalyItalyItaly  156.0  \n",
       "              Spain          SpainSpainSpain  156.0  \n",
       "modern        Austria  AustriaAustriaAustria  150.0  \n",
       "              Czechia  CzechiaCzechiaCzechia  222.0  \n",
       "              England  EnglandEnglandEngland  243.0  \n",
       "              France      FranceFranceFrance  273.0  \n",
       "              Germany  GermanyGermanyGermany  261.0  \n",
       "              RUssia      RUssiaRUssiaRUssia  186.0  \n",
       "              Russia      RussiaRussiaRussia  267.0  \n",
       "              USA                  USAUSAUSA  270.0  \n",
       "post-romantic Austria  AustriaAustriaAustria  216.0  \n",
       "              Finland  FinlandFinlandFinland  276.0  \n",
       "              Germany  GermanyGermanyGermany  255.0  \n",
       "              Italy          ItalyItalyItaly  198.0  \n",
       "renaissance   Belgium  BelgiumBelgiumBelgium  231.0  \n",
       "              England  EnglandEnglandEngland  249.0  \n",
       "              Italy          ItalyItalyItaly  228.0  \n",
       "romantic      Czechia  CzechiaCzechiaCzechia  189.0  \n",
       "              France      FranceFranceFrance  225.0  \n",
       "              Germany  GermanyGermanyGermany  210.0  \n",
       "              Italy          ItalyItalyItaly  264.0  \n",
       "              Russia      RussiaRussiaRussia  162.0  \n",
       "              Spain          SpainSpainSpain  147.0  "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "composer_grouped.apply(mult)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 11.3 Reshaping dataframes\n",
    "\n",
    "As we see above, grouping operations can create more or less complex dataframes by adding one or multiple indexing levels. There are multiple ways to \"reshape\" such dataframes in order to make thm usable e.g. for plotting. Typically, plotting software based on a grammar of graphics expect a simple 2D dataframe where each line is an observation with several properties."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 11.3.1 re-indexing, unstacking\n",
    "\n",
    "One of the most common \"reshaping\" is to reset the index. In its simplest form, it will create a new dataframe, where each row corresponds to one observation. For example in the case of a dataframe with multi-indices, it will re-cast these indices as columns:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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>birth</th>\n",
       "      <th>death</th>\n",
       "      <th>age</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>period</th>\n",
       "      <th>country</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"4\" valign=\"top\">baroque</th>\n",
       "      <th>England</th>\n",
       "      <td>1659.000000</td>\n",
       "      <td>1695.000000</td>\n",
       "      <td>36.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>France</th>\n",
       "      <td>1650.666667</td>\n",
       "      <td>1709.666667</td>\n",
       "      <td>59.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Germany</th>\n",
       "      <td>1685.000000</td>\n",
       "      <td>1754.500000</td>\n",
       "      <td>69.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Italy</th>\n",
       "      <td>1663.000000</td>\n",
       "      <td>1717.250000</td>\n",
       "      <td>54.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"4\" valign=\"top\">classic</th>\n",
       "      <th>Austria</th>\n",
       "      <td>1744.000000</td>\n",
       "      <td>1800.000000</td>\n",
       "      <td>56.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Czechia</th>\n",
       "      <td>1731.000000</td>\n",
       "      <td>1799.000000</td>\n",
       "      <td>68.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Italy</th>\n",
       "      <td>1749.000000</td>\n",
       "      <td>1801.000000</td>\n",
       "      <td>52.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Spain</th>\n",
       "      <td>1754.000000</td>\n",
       "      <td>1806.000000</td>\n",
       "      <td>52.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">modern</th>\n",
       "      <th>Austria</th>\n",
       "      <td>1885.000000</td>\n",
       "      <td>1935.000000</td>\n",
       "      <td>50.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Czechia</th>\n",
       "      <td>1854.000000</td>\n",
       "      <td>1928.000000</td>\n",
       "      <td>74.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       birth        death    age\n",
       "period  country                                 \n",
       "baroque England  1659.000000  1695.000000  36.00\n",
       "        France   1650.666667  1709.666667  59.00\n",
       "        Germany  1685.000000  1754.500000  69.50\n",
       "        Italy    1663.000000  1717.250000  54.25\n",
       "classic Austria  1744.000000  1800.000000  56.00\n",
       "        Czechia  1731.000000  1799.000000  68.00\n",
       "        Italy    1749.000000  1801.000000  52.00\n",
       "        Spain    1754.000000  1806.000000  52.00\n",
       "modern  Austria  1885.000000  1935.000000  50.00\n",
       "        Czechia  1854.000000  1928.000000  74.00"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "composer_grouped = composers.groupby(['period','country']).mean()\n",
    "composer_grouped.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>period</th>\n",
       "      <th>country</th>\n",
       "      <th>birth</th>\n",
       "      <th>death</th>\n",
       "      <th>age</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>baroque</td>\n",
       "      <td>England</td>\n",
       "      <td>1659.000000</td>\n",
       "      <td>1695.000000</td>\n",
       "      <td>36.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>baroque</td>\n",
       "      <td>France</td>\n",
       "      <td>1650.666667</td>\n",
       "      <td>1709.666667</td>\n",
       "      <td>59.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>baroque</td>\n",
       "      <td>Germany</td>\n",
       "      <td>1685.000000</td>\n",
       "      <td>1754.500000</td>\n",
       "      <td>69.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>baroque</td>\n",
       "      <td>Italy</td>\n",
       "      <td>1663.000000</td>\n",
       "      <td>1717.250000</td>\n",
       "      <td>54.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>classic</td>\n",
       "      <td>Austria</td>\n",
       "      <td>1744.000000</td>\n",
       "      <td>1800.000000</td>\n",
       "      <td>56.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    period  country        birth        death    age\n",
       "0  baroque  England  1659.000000  1695.000000  36.00\n",
       "1  baroque   France  1650.666667  1709.666667  59.00\n",
       "2  baroque  Germany  1685.000000  1754.500000  69.50\n",
       "3  baroque    Italy  1663.000000  1717.250000  54.25\n",
       "4  classic  Austria  1744.000000  1800.000000  56.00"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "composer_grouped.reset_index().head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One can of course be more specific and reset only specific indices e.g. by level: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\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>country</th>\n",
       "      <th>birth</th>\n",
       "      <th>death</th>\n",
       "      <th>age</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>period</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>baroque</th>\n",
       "      <td>England</td>\n",
       "      <td>1659.000000</td>\n",
       "      <td>1695.000000</td>\n",
       "      <td>36.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>baroque</th>\n",
       "      <td>France</td>\n",
       "      <td>1650.666667</td>\n",
       "      <td>1709.666667</td>\n",
       "      <td>59.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>baroque</th>\n",
       "      <td>Germany</td>\n",
       "      <td>1685.000000</td>\n",
       "      <td>1754.500000</td>\n",
       "      <td>69.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>baroque</th>\n",
       "      <td>Italy</td>\n",
       "      <td>1663.000000</td>\n",
       "      <td>1717.250000</td>\n",
       "      <td>54.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>classic</th>\n",
       "      <td>Austria</td>\n",
       "      <td>1744.000000</td>\n",
       "      <td>1800.000000</td>\n",
       "      <td>56.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         country        birth        death    age\n",
       "period                                           \n",
       "baroque  England  1659.000000  1695.000000  36.00\n",
       "baroque   France  1650.666667  1709.666667  59.00\n",
       "baroque  Germany  1685.000000  1754.500000  69.50\n",
       "baroque    Italy  1663.000000  1717.250000  54.25\n",
       "classic  Austria  1744.000000  1800.000000  56.00"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "composer_grouped.reset_index(level=1).head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 11.3.2 unstacking\n",
    "Another way to move indices to columns is to *unstack* a dataframe, in other words pivot some indices to columns:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <th colspan=\"10\" halign=\"left\">birth</th>\n",
       "      <th>...</th>\n",
       "      <th colspan=\"10\" halign=\"left\">age</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>country</th>\n",
       "      <th>Austria</th>\n",
       "      <th>Belgium</th>\n",
       "      <th>Czechia</th>\n",
       "      <th>England</th>\n",
       "      <th>Finland</th>\n",
       "      <th>France</th>\n",
       "      <th>Germany</th>\n",
       "      <th>Italy</th>\n",
       "      <th>RUssia</th>\n",
       "      <th>Russia</th>\n",
       "      <th>...</th>\n",
       "      <th>Czechia</th>\n",
       "      <th>England</th>\n",
       "      <th>Finland</th>\n",
       "      <th>France</th>\n",
       "      <th>Germany</th>\n",
       "      <th>Italy</th>\n",
       "      <th>RUssia</th>\n",
       "      <th>Russia</th>\n",
       "      <th>Spain</th>\n",
       "      <th>USA</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>period</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",
       "      <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",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>baroque</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1659.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1650.666667</td>\n",
       "      <td>1685.0</td>\n",
       "      <td>1663.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>36.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>59.000000</td>\n",
       "      <td>69.50</td>\n",
       "      <td>54.25</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>classic</th>\n",
       "      <td>1744.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1731.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1749.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>68.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>52.00</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>52.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>modern</th>\n",
       "      <td>1885.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1854.0</td>\n",
       "      <td>1936.5</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1916.500000</td>\n",
       "      <td>1895.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1891.0</td>\n",
       "      <td>1894.0</td>\n",
       "      <td>...</td>\n",
       "      <td>74.0</td>\n",
       "      <td>81.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>87.500000</td>\n",
       "      <td>87.00</td>\n",
       "      <td>NaN</td>\n",
       "      <td>62.0</td>\n",
       "      <td>79.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>81.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>post-romantic</th>\n",
       "      <td>1842.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1865.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1864.0</td>\n",
       "      <td>1858.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>92.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>85.00</td>\n",
       "      <td>66.00</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>renaissance</th>\n",
       "      <td>NaN</td>\n",
       "      <td>1464.5</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1551.5</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1552.666667</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>73.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>64.00</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>romantic</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1832.5</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1821.000000</td>\n",
       "      <td>1806.5</td>\n",
       "      <td>1817.250000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1836.0</td>\n",
       "      <td>...</td>\n",
       "      <td>61.5</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>70.333333</td>\n",
       "      <td>59.25</td>\n",
       "      <td>58.50</td>\n",
       "      <td>NaN</td>\n",
       "      <td>48.0</td>\n",
       "      <td>49.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>6 rows × 36 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                birth                                                       \\\n",
       "country       Austria Belgium Czechia England Finland       France Germany   \n",
       "period                                                                       \n",
       "baroque           NaN     NaN     NaN  1659.0     NaN  1650.666667  1685.0   \n",
       "classic        1744.0     NaN  1731.0     NaN     NaN          NaN     NaN   \n",
       "modern         1885.0     NaN  1854.0  1936.5     NaN  1916.500000  1895.0   \n",
       "post-romantic  1842.0     NaN     NaN     NaN  1865.0          NaN  1864.0   \n",
       "renaissance       NaN  1464.5     NaN  1551.5     NaN          NaN     NaN   \n",
       "romantic          NaN     NaN  1832.5     NaN     NaN  1821.000000  1806.5   \n",
       "\n",
       "                                            ...     age                  \\\n",
       "country              Italy  RUssia  Russia  ... Czechia England Finland   \n",
       "period                                      ...                           \n",
       "baroque        1663.000000     NaN     NaN  ...     NaN    36.0     NaN   \n",
       "classic        1749.000000     NaN     NaN  ...    68.0     NaN     NaN   \n",
       "modern                 NaN  1891.0  1894.0  ...    74.0    81.0     NaN   \n",
       "post-romantic  1858.000000     NaN     NaN  ...     NaN     NaN    92.0   \n",
       "renaissance    1552.666667     NaN     NaN  ...     NaN    73.0     NaN   \n",
       "romantic       1817.250000     NaN  1836.0  ...    61.5     NaN     NaN   \n",
       "\n",
       "                                                                   \n",
       "country           France Germany  Italy RUssia Russia Spain   USA  \n",
       "period                                                             \n",
       "baroque        59.000000   69.50  54.25    NaN    NaN   NaN   NaN  \n",
       "classic              NaN     NaN  52.00    NaN    NaN  52.0   NaN  \n",
       "modern         87.500000   87.00    NaN   62.0   79.0   NaN  81.0  \n",
       "post-romantic        NaN   85.00  66.00    NaN    NaN   NaN   NaN  \n",
       "renaissance          NaN     NaN  64.00    NaN    NaN   NaN   NaN  \n",
       "romantic       70.333333   59.25  58.50    NaN   48.0  49.0   NaN  \n",
       "\n",
       "[6 rows x 36 columns]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "composer_grouped.unstack()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This creates a multi-level column indexing. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 11.3.3 Wide to long: melt\n",
    "\n",
    "A very common operation when handling tables is to switch from wide to long format and vice versa. In our composer example, let's for example imagine that you want both ```birth``` and ```death``` dates to be grouped in a single column called ```dates```. But you still need to know if that data is a birth or date, so you need a new column that indicates that. To achieve that, we need to specify ```id_vars``` a list of columns to be used as *identifiers* e.g. the composer name, and ```value_vars```, a list of columns that should become rows: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "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>composer</th>\n",
       "      <th>birth</th>\n",
       "      <th>death</th>\n",
       "      <th>period</th>\n",
       "      <th>country</th>\n",
       "      <th>age</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Mahler</td>\n",
       "      <td>1860</td>\n",
       "      <td>1911.0</td>\n",
       "      <td>post-romantic</td>\n",
       "      <td>Austria</td>\n",
       "      <td>51.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Beethoven</td>\n",
       "      <td>1770</td>\n",
       "      <td>1827.0</td>\n",
       "      <td>romantic</td>\n",
       "      <td>Germany</td>\n",
       "      <td>57.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Puccini</td>\n",
       "      <td>1858</td>\n",
       "      <td>1924.0</td>\n",
       "      <td>post-romantic</td>\n",
       "      <td>Italy</td>\n",
       "      <td>66.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Shostakovich</td>\n",
       "      <td>1906</td>\n",
       "      <td>1975.0</td>\n",
       "      <td>modern</td>\n",
       "      <td>Russia</td>\n",
       "      <td>69.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Verdi</td>\n",
       "      <td>1813</td>\n",
       "      <td>1901.0</td>\n",
       "      <td>romantic</td>\n",
       "      <td>Italy</td>\n",
       "      <td>88.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       composer  birth   death         period  country   age\n",
       "0        Mahler   1860  1911.0  post-romantic  Austria  51.0\n",
       "1     Beethoven   1770  1827.0       romantic  Germany  57.0\n",
       "2       Puccini   1858  1924.0  post-romantic    Italy  66.0\n",
       "3  Shostakovich   1906  1975.0         modern   Russia  69.0\n",
       "4         Verdi   1813  1901.0       romantic    Italy  88.0"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "composers.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "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>composer</th>\n",
       "      <th>variable</th>\n",
       "      <th>value</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Mahler</td>\n",
       "      <td>birth</td>\n",
       "      <td>1860.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Beethoven</td>\n",
       "      <td>birth</td>\n",
       "      <td>1770.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Puccini</td>\n",
       "      <td>birth</td>\n",
       "      <td>1858.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Shostakovich</td>\n",
       "      <td>birth</td>\n",
       "      <td>1906.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Verdi</td>\n",
       "      <td>birth</td>\n",
       "      <td>1813.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>109</th>\n",
       "      <td>Smetana</td>\n",
       "      <td>death</td>\n",
       "      <td>1884.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>110</th>\n",
       "      <td>Janacek</td>\n",
       "      <td>death</td>\n",
       "      <td>1928.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>111</th>\n",
       "      <td>Copland</td>\n",
       "      <td>death</td>\n",
       "      <td>1990.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>112</th>\n",
       "      <td>Bernstein</td>\n",
       "      <td>death</td>\n",
       "      <td>1990.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>113</th>\n",
       "      <td>Glass</td>\n",
       "      <td>death</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>114 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         composer variable   value\n",
       "0          Mahler    birth  1860.0\n",
       "1       Beethoven    birth  1770.0\n",
       "2         Puccini    birth  1858.0\n",
       "3    Shostakovich    birth  1906.0\n",
       "4           Verdi    birth  1813.0\n",
       "..            ...      ...     ...\n",
       "109       Smetana    death  1884.0\n",
       "110       Janacek    death  1928.0\n",
       "111       Copland    death  1990.0\n",
       "112     Bernstein    death  1990.0\n",
       "113         Glass    death     NaN\n",
       "\n",
       "[114 rows x 3 columns]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.melt(composers, id_vars=['composer'], value_vars=['birth', 'death'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can keep more of the original columns as *identifiers* and also specify names for the *variable* and *value* columns:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "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>composer</th>\n",
       "      <th>period</th>\n",
       "      <th>age</th>\n",
       "      <th>country</th>\n",
       "      <th>date_type</th>\n",
       "      <th>dates</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Mahler</td>\n",
       "      <td>post-romantic</td>\n",
       "      <td>51.0</td>\n",
       "      <td>Austria</td>\n",
       "      <td>birth</td>\n",
       "      <td>1860.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Beethoven</td>\n",
       "      <td>romantic</td>\n",
       "      <td>57.0</td>\n",
       "      <td>Germany</td>\n",
       "      <td>birth</td>\n",
       "      <td>1770.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Puccini</td>\n",
       "      <td>post-romantic</td>\n",
       "      <td>66.0</td>\n",
       "      <td>Italy</td>\n",
       "      <td>birth</td>\n",
       "      <td>1858.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Shostakovich</td>\n",
       "      <td>modern</td>\n",
       "      <td>69.0</td>\n",
       "      <td>Russia</td>\n",
       "      <td>birth</td>\n",
       "      <td>1906.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Verdi</td>\n",
       "      <td>romantic</td>\n",
       "      <td>88.0</td>\n",
       "      <td>Italy</td>\n",
       "      <td>birth</td>\n",
       "      <td>1813.0</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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>109</th>\n",
       "      <td>Smetana</td>\n",
       "      <td>romantic</td>\n",
       "      <td>60.0</td>\n",
       "      <td>Czechia</td>\n",
       "      <td>death</td>\n",
       "      <td>1884.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>110</th>\n",
       "      <td>Janacek</td>\n",
       "      <td>modern</td>\n",
       "      <td>74.0</td>\n",
       "      <td>Czechia</td>\n",
       "      <td>death</td>\n",
       "      <td>1928.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>111</th>\n",
       "      <td>Copland</td>\n",
       "      <td>modern</td>\n",
       "      <td>90.0</td>\n",
       "      <td>USA</td>\n",
       "      <td>death</td>\n",
       "      <td>1990.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>112</th>\n",
       "      <td>Bernstein</td>\n",
       "      <td>modern</td>\n",
       "      <td>72.0</td>\n",
       "      <td>USA</td>\n",
       "      <td>death</td>\n",
       "      <td>1990.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>113</th>\n",
       "      <td>Glass</td>\n",
       "      <td>modern</td>\n",
       "      <td>NaN</td>\n",
       "      <td>USA</td>\n",
       "      <td>death</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>114 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         composer         period   age  country date_type   dates\n",
       "0          Mahler  post-romantic  51.0  Austria     birth  1860.0\n",
       "1       Beethoven       romantic  57.0  Germany     birth  1770.0\n",
       "2         Puccini  post-romantic  66.0    Italy     birth  1858.0\n",
       "3    Shostakovich         modern  69.0   Russia     birth  1906.0\n",
       "4           Verdi       romantic  88.0    Italy     birth  1813.0\n",
       "..            ...            ...   ...      ...       ...     ...\n",
       "109       Smetana       romantic  60.0  Czechia     death  1884.0\n",
       "110       Janacek         modern  74.0  Czechia     death  1928.0\n",
       "111       Copland         modern  90.0      USA     death  1990.0\n",
       "112     Bernstein         modern  72.0      USA     death  1990.0\n",
       "113         Glass         modern   NaN      USA     death     NaN\n",
       "\n",
       "[114 rows x 6 columns]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "melted = pd.melt(composers, id_vars=['composer','period','age','country'], value_vars=['birth', 'death'],\n",
    "                var_name = 'date_type', value_name='dates')\n",
    "melted"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 11.4 Plotting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have seen above that we can create groups and apply functions to them to get some summary of them as new dataframes or series that could then also be reshaped. The final result of these operations is then ideally suited to be plotted in a very efficient way.\n",
    "\n",
    "Here's a simple example: we group composers by periods and then calculate the mean age, resulting in a series where periods are indices:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "period\n",
       "baroque          56.900000\n",
       "classic          56.800000\n",
       "modern           77.181818\n",
       "post-romantic    73.200000\n",
       "renaissance      68.142857\n",
       "romantic         58.764706\n",
       "Name: age, dtype: float64"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "composers.groupby('period')['age'].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can just add one more operation to that line to create a bar plot illustrating this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "composers.groupby('period')['age'].mean().plot(kind = 'bar');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The built-in plotting capabilities of Pandas automatically used the indices to label the bars, and also used the series name as a general label."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using more advanced libraries, we can go further than that and use multiple columns to create complex plots. This will be shown in the next chapter."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}