{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TP3 - Outils numériques pour les Statistiques Descriptives \n",
    "\n",
    "Rappel : les commandes écrites en Python s'exécutent directement dans ce notebook Jupyter avec la commande `Ctrl+Entrée`, ou `Shift+Entrée` pour passer directement à la cellule suivante.\n",
    "\n",
    "Le but de ce TP3 est d’effectuer des calculs et de tracer des graphiques sur plusieurs sous-\n",
    "groupes, parfois appelés **classes** ou **strates**, d’une même population afin de comparer ces sous-groupes, entre eux ou à la population totale."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# On importe tous les noms des bibliothèques qui nous seront utiles.\n",
    "from pandas import *  # Pour lire, importer et manipuler le tableau de données.\n",
    "from numpy import *  # pour faire des calculs.\n",
    "from matplotlib.pylab import * # Pour faire des graphiques"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(181, 14)\n"
     ]
    },
    {
     "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>Country</th>\n",
       "      <th>SDGi</th>\n",
       "      <th>Life Expectancy</th>\n",
       "      <th>HDI</th>\n",
       "      <th>Per Capita GDP</th>\n",
       "      <th>Region</th>\n",
       "      <th>Income Group</th>\n",
       "      <th>Population (millions)</th>\n",
       "      <th>Total Ecological Footprint (Production)</th>\n",
       "      <th>Total Ecological Footprint (Consumption)</th>\n",
       "      <th>Total biocapacity</th>\n",
       "      <th>Ecological (Deficit) or Reserve</th>\n",
       "      <th>Number of Earths required</th>\n",
       "      <th>Number of Countries required</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>51.847886</td>\n",
       "      <td>63.565</td>\n",
       "      <td>0.488</td>\n",
       "      <td>2439.68</td>\n",
       "      <td>Middle East/Central Asia</td>\n",
       "      <td>LI</td>\n",
       "      <td>38.042</td>\n",
       "      <td>0.750444</td>\n",
       "      <td>0.885011</td>\n",
       "      <td>0.578479</td>\n",
       "      <td>-0.306532</td>\n",
       "      <td>0.570763</td>\n",
       "      <td>1.529894</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Albania</td>\n",
       "      <td>71.486061</td>\n",
       "      <td>79.282</td>\n",
       "      <td>0.81</td>\n",
       "      <td>13862.6</td>\n",
       "      <td>Other Europe</td>\n",
       "      <td>UM</td>\n",
       "      <td>2.881</td>\n",
       "      <td>1.566569</td>\n",
       "      <td>2.102276</td>\n",
       "      <td>1.124433</td>\n",
       "      <td>-0.977842</td>\n",
       "      <td>1.355804</td>\n",
       "      <td>1.869631</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Algeria</td>\n",
       "      <td>70.510917</td>\n",
       "      <td>76.474</td>\n",
       "      <td>0.748</td>\n",
       "      <td>11412.2</td>\n",
       "      <td>Africa</td>\n",
       "      <td>UM</td>\n",
       "      <td>43.053</td>\n",
       "      <td>1.812774</td>\n",
       "      <td>2.367408</td>\n",
       "      <td>0.702314</td>\n",
       "      <td>-1.665094</td>\n",
       "      <td>1.526794</td>\n",
       "      <td>3.370868</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Angola</td>\n",
       "      <td>50.974803</td>\n",
       "      <td>62.448</td>\n",
       "      <td>0.595</td>\n",
       "      <td>7034.84</td>\n",
       "      <td>Africa</td>\n",
       "      <td>LM</td>\n",
       "      <td>31.825</td>\n",
       "      <td>0.686062</td>\n",
       "      <td>1.006983</td>\n",
       "      <td>1.738573</td>\n",
       "      <td>0.731590</td>\n",
       "      <td>0.649426</td>\n",
       "      <td>0.579201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Antigua and Barbuda</td>\n",
       "      <td>NaN</td>\n",
       "      <td>78.691</td>\n",
       "      <td>0.8</td>\n",
       "      <td>22000.2</td>\n",
       "      <td>Central America/Caribbean</td>\n",
       "      <td>HI</td>\n",
       "      <td>0.097</td>\n",
       "      <td>1.541982</td>\n",
       "      <td>3.919553</td>\n",
       "      <td>0.931722</td>\n",
       "      <td>-2.987832</td>\n",
       "      <td>2.527807</td>\n",
       "      <td>4.206785</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               Country       SDGi Life Expectancy    HDI Per Capita GDP  \\\n",
       "0          Afghanistan  51.847886          63.565  0.488        2439.68   \n",
       "1              Albania  71.486061          79.282   0.81        13862.6   \n",
       "2              Algeria  70.510917          76.474  0.748        11412.2   \n",
       "3               Angola  50.974803          62.448  0.595        7034.84   \n",
       "4  Antigua and Barbuda        NaN          78.691    0.8        22000.2   \n",
       "\n",
       "                      Region Income Group  Population (millions)  \\\n",
       "0   Middle East/Central Asia           LI                 38.042   \n",
       "1               Other Europe           UM                  2.881   \n",
       "2                     Africa           UM                 43.053   \n",
       "3                     Africa           LM                 31.825   \n",
       "4  Central America/Caribbean           HI                  0.097   \n",
       "\n",
       "   Total Ecological Footprint (Production)  \\\n",
       "0                                 0.750444   \n",
       "1                                 1.566569   \n",
       "2                                 1.812774   \n",
       "3                                 0.686062   \n",
       "4                                 1.541982   \n",
       "\n",
       "   Total Ecological Footprint (Consumption)  Total biocapacity   \\\n",
       "0                                  0.885011            0.578479   \n",
       "1                                  2.102276            1.124433   \n",
       "2                                  2.367408            0.702314   \n",
       "3                                  1.006983            1.738573   \n",
       "4                                  3.919553            0.931722   \n",
       "\n",
       "   Ecological (Deficit) or Reserve  Number of Earths required  \\\n",
       "0                        -0.306532                   0.570763   \n",
       "1                        -0.977842                   1.355804   \n",
       "2                        -1.665094                   1.526794   \n",
       "3                         0.731590                   0.649426   \n",
       "4                        -2.987832                   2.527807   \n",
       "\n",
       "   Number of Countries required  \n",
       "0                      1.529894  \n",
       "1                      1.869631  \n",
       "2                      3.370868  \n",
       "3                      0.579201  \n",
       "4                      4.206785  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Importation des données dans un dataframe\n",
    "df = read_excel('footprint.xlsx')\n",
    "print(shape(df)) # Affiche le nombre de pays et le nombre de variables (en\n",
    "# comptabilisant le nom du pays comme une variable).\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercice 0\n",
    "Chercher les définitions de chacune des variables et exécuter le bloc suivant visant à renommer les colonnes pour plus de simplicité."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>PAYS</th>\n",
       "      <th>SDG</th>\n",
       "      <th>LIFE</th>\n",
       "      <th>HDI</th>\n",
       "      <th>GDP</th>\n",
       "      <th>REG</th>\n",
       "      <th>IC</th>\n",
       "      <th>POP</th>\n",
       "      <th>PROD</th>\n",
       "      <th>CONSU</th>\n",
       "      <th>BCAP</th>\n",
       "      <th>ECO</th>\n",
       "      <th>NEARTH</th>\n",
       "      <th>NCOUNT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>51.847886</td>\n",
       "      <td>63.565</td>\n",
       "      <td>0.488</td>\n",
       "      <td>2439.68</td>\n",
       "      <td>Middle East/Central Asia</td>\n",
       "      <td>LI</td>\n",
       "      <td>38.042</td>\n",
       "      <td>0.750444</td>\n",
       "      <td>0.885011</td>\n",
       "      <td>0.578479</td>\n",
       "      <td>-0.306532</td>\n",
       "      <td>0.570763</td>\n",
       "      <td>1.529894</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Albania</td>\n",
       "      <td>71.486061</td>\n",
       "      <td>79.282</td>\n",
       "      <td>0.81</td>\n",
       "      <td>13862.6</td>\n",
       "      <td>Other Europe</td>\n",
       "      <td>UM</td>\n",
       "      <td>2.881</td>\n",
       "      <td>1.566569</td>\n",
       "      <td>2.102276</td>\n",
       "      <td>1.124433</td>\n",
       "      <td>-0.977842</td>\n",
       "      <td>1.355804</td>\n",
       "      <td>1.869631</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Algeria</td>\n",
       "      <td>70.510917</td>\n",
       "      <td>76.474</td>\n",
       "      <td>0.748</td>\n",
       "      <td>11412.2</td>\n",
       "      <td>Africa</td>\n",
       "      <td>UM</td>\n",
       "      <td>43.053</td>\n",
       "      <td>1.812774</td>\n",
       "      <td>2.367408</td>\n",
       "      <td>0.702314</td>\n",
       "      <td>-1.665094</td>\n",
       "      <td>1.526794</td>\n",
       "      <td>3.370868</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Angola</td>\n",
       "      <td>50.974803</td>\n",
       "      <td>62.448</td>\n",
       "      <td>0.595</td>\n",
       "      <td>7034.84</td>\n",
       "      <td>Africa</td>\n",
       "      <td>LM</td>\n",
       "      <td>31.825</td>\n",
       "      <td>0.686062</td>\n",
       "      <td>1.006983</td>\n",
       "      <td>1.738573</td>\n",
       "      <td>0.731590</td>\n",
       "      <td>0.649426</td>\n",
       "      <td>0.579201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Antigua and Barbuda</td>\n",
       "      <td>NaN</td>\n",
       "      <td>78.691</td>\n",
       "      <td>0.8</td>\n",
       "      <td>22000.2</td>\n",
       "      <td>Central America/Caribbean</td>\n",
       "      <td>HI</td>\n",
       "      <td>0.097</td>\n",
       "      <td>1.541982</td>\n",
       "      <td>3.919553</td>\n",
       "      <td>0.931722</td>\n",
       "      <td>-2.987832</td>\n",
       "      <td>2.527807</td>\n",
       "      <td>4.206785</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  PAYS        SDG    LIFE    HDI      GDP  \\\n",
       "0          Afghanistan  51.847886  63.565  0.488  2439.68   \n",
       "1              Albania  71.486061  79.282   0.81  13862.6   \n",
       "2              Algeria  70.510917  76.474  0.748  11412.2   \n",
       "3               Angola  50.974803  62.448  0.595  7034.84   \n",
       "4  Antigua and Barbuda        NaN  78.691    0.8  22000.2   \n",
       "\n",
       "                         REG  IC     POP      PROD     CONSU      BCAP  \\\n",
       "0   Middle East/Central Asia  LI  38.042  0.750444  0.885011  0.578479   \n",
       "1               Other Europe  UM   2.881  1.566569  2.102276  1.124433   \n",
       "2                     Africa  UM  43.053  1.812774  2.367408  0.702314   \n",
       "3                     Africa  LM  31.825  0.686062  1.006983  1.738573   \n",
       "4  Central America/Caribbean  HI   0.097  1.541982  3.919553  0.931722   \n",
       "\n",
       "        ECO    NEARTH    NCOUNT  \n",
       "0 -0.306532  0.570763  1.529894  \n",
       "1 -0.977842  1.355804  1.869631  \n",
       "2 -1.665094  1.526794  3.370868  \n",
       "3  0.731590  0.649426  0.579201  \n",
       "4 -2.987832  2.527807  4.206785  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# On renomme les noms des colonnes.\n",
    "colonnes = [\n",
    "    \"PAYS\",\"SDG\",\"LIFE\",\"HDI\",\"GDP\",\"REG\",\"IC\",\"POP\",\n",
    "    \"PROD\",\"CONSU\",\"BCAP\",\"ECO\",\"NEARTH\",\"NCOUNT\"\n",
    "]\n",
    "df.columns = colonnes\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercice 1 \n",
    "\n",
    "**Question 1.** La classe dataframe de la bibliothèque Panda permet de sélectionner des données de\n",
    "manière assez simple et intuitive, et de faire des calculs. Exécuter les cellules ci-dessous et observer les résultats. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Voici les 3 premières lignes de df:\n",
      "          PAYS        SDG    LIFE    HDI      GDP                       REG  \\\n",
      "0  Afghanistan  51.847886  63.565  0.488  2439.68  Middle East/Central Asia   \n",
      "1      Albania  71.486061  79.282   0.81  13862.6              Other Europe   \n",
      "2      Algeria  70.510917  76.474  0.748  11412.2                    Africa   \n",
      "\n",
      "   IC     POP      PROD     CONSU      BCAP       ECO    NEARTH    NCOUNT  \n",
      "0  LI  38.042  0.750444  0.885011  0.578479 -0.306532  0.570763  1.529894  \n",
      "1  UM   2.881  1.566569  2.102276  1.124433 -0.977842  1.355804  1.869631  \n",
      "2  UM  43.053  1.812774  2.367408  0.702314 -1.665094  1.526794  3.370868  \n",
      "Voici les 3 premières lignes de la colonne POP de df:\n",
      "0    38.042\n",
      "1     2.881\n",
      "2    43.053\n",
      "Name: POP, dtype: float64\n",
      "Voici la colonne POP des 3 premières lignes de df:\n",
      "0    38.042\n",
      "1     2.881\n",
      "2    43.053\n",
      "Name: POP, dtype: float64\n",
      "Le type de pop est <class 'pandas.Series'> et le type de X est <class 'numpy.ndarray'>\n",
      "Comparer les 3 premières lignes de pop ci-dessous ...\n",
      "0    38.042\n",
      "1     2.881\n",
      "2    43.053\n",
      "Name: POP, dtype: float64\n",
      "... avec les 3 premières lignes de X ci-dessous :\n",
      "[38.042  2.881 43.053]\n"
     ]
    }
   ],
   "source": [
    "# Exécuter, observer les lignes d'instruction ci-dessous\n",
    "print(\"Voici les 3 premières lignes de df:\")\n",
    "print(df[0:3])\n",
    "print(\"Voici les 3 premières lignes de la colonne POP de df:\")\n",
    "print(df.POP[0:3])\n",
    "print(\"Voici la colonne POP des 3 premières lignes de df:\")\n",
    "print(df[0:3].POP)\n",
    "pop = df.POP\n",
    "X = df.POP.values\n",
    "print(\"Le type de pop est\", type(pop), \"et le type de X est\", type(X))\n",
    "print(\"Comparer les 3 premières lignes de pop ci-dessous ...\")\n",
    "print(pop[0:3])\n",
    "print(\"... avec les 3 premières lignes de X ci-dessous :\")\n",
    "print(X[0:3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "42.39262430939226 23380.918212974877\n",
      "42.39262430939226 23380.918212974877\n"
     ]
    }
   ],
   "source": [
    "# Exécuter, observer et commenter les lignes d'instruction ci-dessous\n",
    "print(mean(df.POP), var(df.POP))\n",
    "print(mean(X), var(X))\n",
    "# Commentaire. Les fonctions mean et var de numpy s'appliquent indistinctement\n",
    "# sur des pandas.Series et sur des numpy.ndarray."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Que se passe-t-il avec l'instruction ci-dessous? Commenter.\n",
    "#print(mean(df.REG.values)) # On a pris soin de désactiver cette instruction.\n",
    "# L'instruction déclenche une erreur car elle est invalide. En effet, il n'est\n",
    "# pas possible de calculer la moyenne d'une variable qualitative (ici la\n",
    "# variable REG correspondant aux noms des régions (type chaîne de caractères))."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 2.** Observer dans la cellule ci-dessous l’utilisation des booléens pour sélectionner des données. Rappel : la variable POP donne la population en millions d’habitants."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "14\n",
      "                         PAYS        SDG       LIFE    HDI      GDP  \\\n",
      "11                 Bangladesh  63.417508     72.806  0.644  5113.78   \n",
      "21                     Brazil  72.682032     75.338  0.766  14799.5   \n",
      "33                      China  71.980012     77.968  0.762    15893   \n",
      "49                      Egypt  67.570268     71.358  0.735  11940.2   \n",
      "55                   Ethiopia  56.399547     65.838  0.498  2641.01   \n",
      "76                      India   60.38518      70.91  0.645  6683.45   \n",
      "77                  Indonesia  68.416705     70.518  0.716  11976.5   \n",
      "84                      Japan  79.319742  84.356341  0.924  41723.6   \n",
      "107                    Mexico  70.337857     74.202  0.779  19925.8   \n",
      "119                   Nigeria  54.066445      52.91  0.538  5135.49   \n",
      "122                  Pakistan  59.151852     66.756  0.546  5412.61   \n",
      "127               Philippines   66.66352     71.865  0.718  8983.41   \n",
      "135        Russian Federation  73.696452  73.083902  0.845  27341.1   \n",
      "172  United States of America  74.402211  78.787805   0.93  62417.6   \n",
      "\n",
      "               REG  IC       POP      PROD     CONSU      BCAP       ECO  \\\n",
      "11    Asia-Pacific  LI   163.046  0.485815  0.708539  0.252668 -0.455870   \n",
      "21   South America  UM   211.050  3.322804  2.600708  8.294001  5.693293   \n",
      "33    Asia-Pacific  UM  1465.634  3.230469  3.510020  0.798626 -2.711394   \n",
      "49          Africa  LM   100.388  1.081353  1.617001  0.314186 -1.302815   \n",
      "55          Africa  LI   112.079  0.865362  0.903794  0.478106 -0.425688   \n",
      "76    Asia-Pacific  LM  1366.418  1.017207  1.069030  0.355736 -0.713294   \n",
      "77    Asia-Pacific  LM   270.626  1.845979  1.683977  1.246901 -0.437076   \n",
      "84    Asia-Pacific  HI   126.860  3.381101  4.235759  0.631134 -3.604625   \n",
      "107  North America  UM   127.576  2.114546  2.520611  1.243432 -1.277179   \n",
      "119         Africa  LM   200.964  0.768103  0.850849  0.480522 -0.370328   \n",
      "122   Asia-Pacific  LM   216.565  0.690093  0.705300  0.366391 -0.338909   \n",
      "127   Asia-Pacific  LM   108.117  0.946925  1.283765  0.415587 -0.868178   \n",
      "135   Other Europe  UM   145.872  7.144748  5.816537  7.545711  1.729174   \n",
      "172  North America  HI   329.065  7.666494  7.776182  3.722449 -4.053733   \n",
      "\n",
      "       NEARTH    NCOUNT  \n",
      "11   0.456952  2.804223  \n",
      "21   1.677254  0.313565  \n",
      "33   2.263690  4.395076  \n",
      "49   1.042840  5.146639  \n",
      "55   0.582877  1.890362  \n",
      "76   0.689441  3.005125  \n",
      "77   1.086034  1.350530  \n",
      "84   2.731735  6.711350  \n",
      "107  1.625598  2.027140  \n",
      "119  0.548732  1.770679  \n",
      "122  0.454864  1.924992  \n",
      "127  0.827928  3.089044  \n",
      "135  3.751214  0.770840  \n",
      "172  5.015033  2.088996  \n",
      "11                   Bangladesh\n",
      "21                       Brazil\n",
      "33                        China\n",
      "49                        Egypt\n",
      "55                     Ethiopia\n",
      "76                        India\n",
      "77                    Indonesia\n",
      "84                        Japan\n",
      "107                      Mexico\n",
      "119                     Nigeria\n",
      "122                    Pakistan\n",
      "127                 Philippines\n",
      "135          Russian Federation\n",
      "172    United States of America\n",
      "Name: PAYS, dtype: str\n"
     ]
    }
   ],
   "source": [
    "# Commenter les lignes d'instruction en précisant ce qui est affiché.\n",
    "print(sum(df.POP>100))  # On affiche le nombre de pays qui ont plus de 100\n",
    "# millions d'habitants.\n",
    "print(df[df.POP>100])   # On affiche le pandas.DataFrame construit à partir de\n",
    "# df en ne gardant que les 14 pays de plus de 100 millions d'habitants.\n",
    "print(df.PAYS[df.POP>100])  # On affiche la colonne PAYS (pandas.Series) du\n",
    "# DataFrame précédent."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 3.** Pour la suite du TP, on va s'intéresser uniquement aux pays de plus d’un million d’habitants, et dans cette question plus particulièrement à la variable LIFE (Life expectancy: espérance de vie) sur l'ensemble de ces pays. Pour cela, commencer par définir un dataframe contenant uniquement les données d'intérêt puis compléter les \"print\" ci-dessous."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Nombre de pays de plus d'un million d'habitants : 153\n",
      "Moyenne de la variable LIFE pour ces pays : 72.16\n",
      "Ecart-type de la variable LIFE pour ces pays : 7.85\n",
      "Médiane de la variable LIFE pour ces pays : 73.2\n"
     ]
    }
   ],
   "source": [
    "dfsup1 = df[df.POP>1] # Toutes les données pour les pays de plus d'un million\n",
    "# d'habitants\n",
    "life = dfsup1.LIFE # la variable LIFE pour ces pays\n",
    "print(\"Nombre de pays de plus d'un million d'habitants :\", len(life)) \n",
    "print(\"Moyenne de la variable LIFE pour ces pays :\", round(mean(life), 2))\n",
    "print(\"Ecart-type de la variable LIFE pour ces pays :\", round(std(life), 2)) \n",
    "print(\"Médiane de la variable LIFE pour ces pays :\", round(median(life), 2)) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercice 2 - Boîte à moustaches\n",
    "\n",
    "On travaille dans cet exercice avec les **données restreintes aux pays de plus d'un million d'habitants**, donc avec le dataframe que vous avez défini précédemment. Cette restriction ne sera plus rappelée !"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 1.** Calculer la médiane et les quartiles de la variable LIFE puis tracer la boîte à moustaches de cette variable en utilisant la fonction `boxplot`. Commenter les résultats. Pour plus de détails, en particuliers concernant les moustaches, aller visiter la page http://python-simple.com/python-matplotlib/boxplot.php."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "65.876\n",
      "73.198\n",
      "78.002\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculer la médiane et les quartiles\n",
    "print(quantile(life, 0.25))\n",
    "print(quantile(life, 0.5))\n",
    "print(quantile(life, 0.75))\n",
    "# Tracer la boîte à moustaches \n",
    "boxplot([life], vert=False)\n",
    "title(\"Espérance de vie des pays de plus d'1 million d'habitants\")\n",
    "show()\n",
    "# Commenter. La boîte au centre du diagramme indique de gauche à droite par un\n",
    "# trait vertical le premier quartile (Q1), la médiane et le troisième quartile\n",
    "# (Q3)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Remarque. Les \"moustaches\" (traits horizontaux à gauche et à droite de la\n",
    "# boîte sont tracées en utilisant la distance interquartile IQ = Q3 - Q1.\n",
    "# - L'extrémité de la moustache gauche est placée par défaut à Q1 - 1.5IQ (ou\n",
    "#   au minimum de la série si min > Q1 - 1.5IQ)\n",
    "# - L'extrémité de la moustache droite est placée par défaut au Q3 + 1.5IQ (ou\n",
    "#   au maximum de la série si max < Q1 - 1.5IQ)\n",
    "# On peut changer arbitrairement 1.5 par un autre facteur comme ci-dessous où\n",
    "# 1.5 a été remplacé par 0.5 grâce au paramètre whis :\n",
    "boxplot([life], vert=False, whis=0.5) # whiskers signifie moustache\n",
    "title(\"Espérance de vie des pays de plus d'1 million d'habitants\")\n",
    "show()\n",
    "# Les points sortant des moustaches sont représentés par des cercles. Avec la\n",
    "# convention par défaut whis=1.5, on considères ces points comme anormaux. Ils\n",
    "# sont dits outliers en anglais. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 2.** Calculer la médiane et les quartiles de la variable POP (sur tous les pays ou sur ceux de plus d'un million d'habitants, peu importe), tracer sa boîte à moustaches. Que constatez-vous ? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.379\n",
      "11.539\n",
      "37.411\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pop = dfsup1.POP\n",
    "# Calculer la médiane et les quartiles\n",
    "print(quantile(pop, 0.25))\n",
    "print(quantile(pop, 0.5))\n",
    "print(quantile(pop, 0.75))\n",
    "# Tracer la boîte à moustaches \n",
    "boxplot([pop], vert=False)\n",
    "title(\"Population des pays de plus d'1 million d'habitants\")\n",
    "show()\n",
    "# Commenter. En raison de l'Inde et la Chine dont les populations sont de plus\n",
    "# d'un milliard d'habitants, le diagramme en boîte est écrasé ce qui n'est pas\n",
    "# informatif. Il faudrait utiliser une échelle logarithmique.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 3.** Comparaison de boîtes à moustaches. Les boîtes à moustaches permettent de comparer visuellement la répartition d'une même variable suivant différentes classes d'une même population. C'est ce qu'on va faire ici pour la variable LIFE (sur l'ensemble des pays de plus d'1 M. d'hab) en fonction des régions (variable REG) auxquelles appartiennent ces pays. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "60.52525\n",
      "62.769999999999996\n",
      "65.95525\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Créer la boîte à moustaches de la variable LIFE uniquement pour les pays de\n",
    "# la région Africa. \n",
    "life_af = life[dfsup1.REG=='Africa']\n",
    "# Calculer la médiane et les quartiles\n",
    "print(quantile(life_af, 0.25))\n",
    "print(quantile(life_af, 0.5))\n",
    "print(quantile(life_af, 0.75))\n",
    "# Tracer la boîte à moustaches \n",
    "boxplot([life_af], vert=False)\n",
    "title(\"Espérance de vie des pays de l'Afrique\")\n",
    "show()\n",
    "# Commenter. En affrique, l'espérance de vie est comprise entre 53 et 72 ans\n",
    "# pour la grande majorité des pays. Quelques pays font exception."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# On va tracer sur le même graphique les boîtes à moustaches de la variable\n",
    "# LIFE pour chacune des régions de la liste reg_labels définie ci-dessous.\n",
    "\n",
    "reg_labels = [\n",
    "    'Africa', 'Asia-Pacific', 'Central America/Caribbean', 'EU-28',\n",
    "    'Middle East/Central Asia', 'Other Europe', 'South America'\n",
    "] \n",
    "\n",
    "# Pourquoi a-t-on exclu la région 'North America' ?\n",
    "# Réponse. Cette région ne contient que 3 pays. En effet :\n",
    "print(len(dfsup1[dfsup1.REG=='North America']))\n",
    "\n",
    "# A vous de tracer le graphique attendu !\n",
    "boxplot(\n",
    "    [life[dfsup1.REG==reg] for reg in reg_labels], # liste de pandas.Series\n",
    "    vert=False,\n",
    "    tick_labels=reg_labels # étiquettes de l'axe des ordonnées\n",
    ")\n",
    "title(\"Espérance de vie des pays par région\")\n",
    "show()\n",
    "# Commenter. Le graphique permet de constater que les pays d'Afrique se\n",
    "# distinguent nettement des autres régions avec une espérance de vie\n",
    "# globalement plus basse. Au sein des autres régions, les régions se\n",
    "# distinguent entre elles par leur variabilité. Par exemple, les pays\n",
    "# d'Amérique du Sud sont plus proches les uns des autres que les pays de\n",
    "# l'Asie-Pacifique."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercice 3. Sous-échantillon\n",
    "Dans cet exercice, on va comparer la moyenne d'un sous-échantillon avec la moyenne de l'échantillon global; on fera de même avec la variance. On va s'intéresser à la variable POP et on commence par retirer les deux \"outlyers\", c'est-à-dire les deux valeurs extrêmes qui sont d'un ordre de grandeur très différent (population de la Chine et population de l'Inde)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "181 179\n",
      "la taille de l échantillon est maintenant : 179\n"
     ]
    }
   ],
   "source": [
    "# On retire du dataframe df les données des deux pays ayant une population\n",
    "# supérieure à 1 milliard d'habitants (l'Inde et la Chine).\n",
    "df2 = df[df.POP<1000]\n",
    "# On vérifie qu'on a bien enlevé deux pays.\n",
    "print(len(df), len(df2))\n",
    "\n",
    "# On convertit en numpy.ndarrays les pandas.Series POP et PAYS du dataframe\n",
    "# df2.\n",
    "POP2 = df2.POP.values # POP2 est une ndarray qui contient les populations des\n",
    "# pays de moins d'un milliard d'habitants.\n",
    "PAYS2 = df2.PAYS.values  # PAYS2 est une ndarray qui contient les noms des pays\n",
    "# de moins d'un milliard d'habitants\n",
    "print('la taille de l échantillon est maintenant :', len(df2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 1.** Calculer la moyenne et la variance de la variable POP2, appelée \"moyenne globale\" et \"variance globale\" dans la suite de l'exercice. Calculer la moyenne et la variance d'un sous-échantillon de taille $n=100$ tiré au hasard parmi les valeurs de POP2. Recommencer et comparer les valeurs obtenues en calculant le quotient \"moyenne sous-échatillon/moyenne globale\" et \"variance sous-échantillon/variance globale\". "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.940046610079337\n",
      "0.7798914651955118\n"
     ]
    }
   ],
   "source": [
    "# Moyenne et variance globales\n",
    "moy_glob = mean(POP2)\n",
    "var_glob = var(POP2)\n",
    "# Sélection aléatoire d'un échantillon de n=100 valeurs de population\n",
    "from random import *\n",
    "n = 100\n",
    "pop2_ech = choices(POP2, k=n)\n",
    "# Moyenne et variance de la variable population prise dans l'échantillon\n",
    "moy_ech = mean(pop2_ech)\n",
    "var_ech = var(pop2_ech)\n",
    "# Quotients \"moyenne de l'échatillon/moyenne globale\" et \"variance de\n",
    "# l'échantillon/variance globale\".\n",
    "print(moy_ech / moy_glob)\n",
    "print(var_ech / var_glob)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 2.** Vous avez dû observer que les résultats obtenus à la question précédente sont fluctuants. Afin de \"lisser\" ces résultats, répéter l'expérience précédente 1000 fois et calculer la moyenne des moyennes des sous-échantillons, appelée \"moyenne empirique\", et la moyenne des variances des sous-échantillons, appelée \"variance empirique\". Comparer la moyenne empirique et la moyenne globale, ainsi que la variance empirique et la variance globale, en calculant les quotients. Recommencer plusieurs fois. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9988758829030208\n",
      "0.9980834269941053\n"
     ]
    }
   ],
   "source": [
    "repet = 1000 # nombre de répétitions : nombre d'échantillons aléatoires\n",
    "# utilisés\n",
    "n = 100 # taille de chacun des 1000 echantillons\n",
    "# Somme des moyennes et variances de la variable population des échantillons\n",
    "# initialisées au départ à zéros\n",
    "acc_moy_echs = 0\n",
    "acc_var_echs = 0\n",
    "\n",
    "for _ in range(repet):\n",
    "    # Choix d'un échantillon aléatoire de n = 100 valeurs de population\n",
    "    pop2_ech = choices(POP2, k=n)\n",
    "    # incrémentation des variables d'accumulation\n",
    "    acc_moy_echs += mean(pop2_ech)\n",
    "    acc_var_echs += var(pop2_ech)\n",
    "\n",
    "# Calcul des moyennes et variances empiriques\n",
    "moy_emp = acc_moy_echs / repet\n",
    "var_emp = acc_var_echs / repet\n",
    "\n",
    "# Calcul et affichage des Ratios \"moyenne empirique/moyenne globale\" et \n",
    "# \"variance empirique/variance globale\".\n",
    "print(moy_emp/moy_glob)\n",
    "print(var_emp/var_glob)\n",
    "\n",
    "# Remarque. On voit que les ratios varient entre chaque exécution de la\n",
    "# cellule. C'est normal, il s'agit de la fluctuation d'échantillonnage :\n",
    "# les variances et moyennes sont tantôt surestimées ou sous-estimées."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 3.** Dans le bloc suivant, on étudie le quotient \"moyenne empirique/moyenne globale\" en fonction de la taille du sous-échantillon ainsi que le quotient \"variance empirique/variance globale\" en fonction de la taille du sous-échantillon. Exécuter les lignes de commande (soyez patient, cela peut prendre un peu de temps), observer et commenter. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
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aajY6+zyi8zVJM+33ilwH9wdhkma0SWu/1WeU9gWrVf5JrdMJMsl6J+IGFnN0iQKmZ1mb/1t2gZ/w6CSV6CydpWfbZE8Sv7aV1kE9las0y/6lskwxBAPOr1bQPA4oYOaVNh/om/8fDgb0SbCvSoKW+gQ/VYn7vJZlIh6XtL7O+uBn1L/kn63LuAGEG0SY57gBRjBgn5lbCf6XilmiXLu0IkUGsK342eRU79XVTuynPmAeoMguVq37XReFNURuhjtLFUQh05G0+cQlLO2xKrUvXKGQFVQoHGy57TegRN17BGVvpECJ7A26Y6e0vlaqb3RewHw8uwNpcx1Gy63zHu5j970C9rzW9w/EPjf2NWP/Fzk/4rVbXsddxn2OUj8/5TJtpjjv0fy/C6yH9VdrhL3M8dYKHdprs6Ze/JGC99zTvJ6tn8/0YWlZ70ZT1VpjByL5vop02sHIa6+9ptNa+8e2tO246KKL9NBDD2nDhg1au3Zty/8PPPBAO/CYPHmyZs6cqerqav3617/WmDGt7TUKiTmgefH2205XYfdg7PV5iapSTA8ft+rBDUgSZW/i8RIMmYOaOWM1Z8LpHPxc9k4ckH7968RX9o0NEI5+b4E+O2eiAg+lPoilOojGywwFFdKpWmqHMCanonNG6ZxzgnGDOJM9eughp6yd72Li8jAf1JTIjptnaMmnz+qUGWOdH88IcQ858dJHSRx7w1l6u8sou4wiIyhTDibt/7TObROM/c+vg6owmQezw8TUU3nZjvGqZeKyLFVsWae7e9+iSXv/yxyRnAO/mVrumyNV8637uPn+ntJKdS3dq0Dk/9zgwUzdyp3HoYbm+RGBRWnAPtDbzzVBQZIzwVjmUDlAez0fvN3XOU5v24fddKR17hlyDwCmcr6bVFGpvQ1dtGlLqRpDpfbBt2toj/YPr3UOmM0Ha5kBI8zjcPPzW6bYx23nNVb01AvhM7R5dw8dFl6lUeGl9muVmOXcg2jzsvYByrQ/s2Jer/lxOBzQNquX+oY/jTngx7x31Px489qWodlvP1FvHagP2uy3ixcn+B1008vmCz15sqwtdXZgnUxD937avUfqG279fn5cUq3t37xER57lIb2bRCBJu5l8a1JQ7+tg++fhAx2i+b+Rguan5JiRCsSeLVZVa82XLtGG7ofabURM1Uw+MyJZ6dqbL9kaZyTd7r9eSqaqSrr0Uungg50zcnNmnmjsBbOskSiD4VZBJDrQex9DJbl4B6O1qrEPYJEHv2QS/kBEMikgc8D0UJDuQXSs5tvrEK99TJvMkJcUU4JVMtzVintwNg2mTeRjIiuzQyRLOw0YIN1zj7OBzUq6G+Rb30recjTyeZGNfwYP1oItozRxSjDqbQ+oDum3lyzVFw6NSANNmSRtrpXKAva0oWyQZne5UivKjle3LrtV2WWvupXtVrcue+z7x3V5Q+eUPWMfcwNuUNEl5jZyfkQwUDDMQbqp+dYcPM1kxoQKSfWhMq0JDdWm0CD7ft/QVh0ZekuVob2ty5tA4IijpD79pB69pb0N0h/+KH26vfn1mg+g7n1z6z4OR7xnOM7/Wu5HvI473XCDdPrpbXZkdzf+eH1IH2qoXf2TUe4h3pemrk7W5MkKROxIVjCoQGSr9zS1t4oymVO1uKW9WFq/h81fbDsYiPi9aQkOJk1yvsujRtm/8f/+5VK7p4h78I0aSyPe70oHc6tu0Es6XR9Wj9L0mcHon8NkbQRyIC/jjHTGYCTRAas93DNaE3BPnZqlA307gyiTUTh3wFLNu2eDXvlgsP5j6iiFA0HPn3fuXGn8+CQ7trtCHr/QtcEaXRVqDYbcWCBBTJE40PEQxcT7rWlzoHeDinvvdaLMTDZaoh3JHOjLA81T8/0h/aWLvyMdfZhUv1Nq2KXwvp3avG6XGnfvUp9dq9Vt8yoF1NAceJise0l++8OZz9DYfOB3b01QYKZG974lq0na3VSpuaHvaEhTrb7Q9Bf1bNrZurwJAL41XjpxpFRaLi1fId03R9q4JSqwaL2NCTzieP+MK3XJwvPsrFoo4szabo9ohfTSLTHb1t0f0giYM+bhqBpqCGnNlHt1yOw021NEiv3SpPps550nPfVU2m8zXZPsqkUj2wHJeM212yi5v5mRmeKU4n2xU/6QJBCTdUl4lpnIlVc6Jxtz5kSvT7zMaWyXyJoa6Re/cJ5vGsaZ9ffYUj82M2NVVyuQ5OQsHwhG2imbwbH7fTDjuH3nO2kc6HMURMX7oqf7ee1j79YkmQnTx9hLqqb5bDE0cpSWvhr0FqynGei0pK8ighNzwEp6cpCsQMxyFSbVHjFN/qF03BHSvm3Svu2t07r3pY/elYJNTuBhnpeDTENYpdq+t5t2N3bT7oZK7W6s1O4G87hSexq72vd7NW3TNxp+5wQSJnhouY28HxlYSOrWS9ryaXNAoIwyXEmDgdgff3NwnDUr/QJYvFgLtp6a3rHIy35khgQ262oOHpkELF6Oqtn4sTEZNtPlzS3XVJ/NrJf5bKn6fCc4625UF10enBPVhqrlIGq++6mygikyI5nGEDk568/k7NQ9OYm3PkbkvJisqGLXuT37R0ZRXXYRjGSBux8tWhTd8NGL2My92be8VqVkkhlJtt/GC7zjfdHNMqlqF1pO8qYvUPBbCTIThlmJiFF3M4q8Ev2wpFMnFU9kVU6oUdrzibS7Ttq9xbm/7CXpsQecIKOyeXKDDnPfZCbay6T0TTfwfZZU3zyZx8Gu0jnjpIqeUpdKaf1m6TePSNt2ye7N2mCWa162oTl42K9K+uBDLXg22GbbR56IfVuP6TF5iIYzSedlmuGKle62jck6pHUs8vpeJsuWYTuClAXQ3sxMoqxLe78jXs66q6oUiAny22Sc7AU9nNEHAqrvX61n7lmjQVXBXNccpM9rQNCeuvZkYnfseC31871OHhGMZNFjj3nLaKQKKlJVpWRrn4ndb1MF3rES/Y60BNmPh3TulBRnXf37S1tMl7cMI69k7UFSpZjMepqgoYc9wIHUPeJ+N3PbHFQM6imF3G5waTIFs0/SXlN90EUaPkrq2keq6CVV9G6+jZn+tVIaf3Fr4JGsTEw0mHaq6tSkJ2KhRUt0+n95PEDFtplJVv8XEXmnleFqb31je8/6vH6xTcBsxj1KZ3tEtFFIWADpZvjS+fxeP5vJYpgRFnOR9UnnAJ7sdQqF++VKVHWS788RSvNsuT1nufloZmF1ANm6am+mzNVPs3XVXPfy27FX8nXnJbpybr7Fu2quuSy7vX5eCyTZ5Wbd67y7172OffN4lzo284IBy7p5smXtH7Sso0st6+Qyy/pKhWV9q6tl/aCbZU3ublk39rCsqT29Tzf3tqy7DrasWcMt656RljW2q2V9tcKyTi23rOFlzvscUmpZQ0osq0/Asioy3GheLxttrhPu9RrtyXa2dC8jbSZzGV9zOd/I7ZLvnTbR+8VOLTtkzGeMd131eLzux+7lj2Nf+8knk3xJcvjD4uW9vL62e2nldPc3L9/jdMrMXG7W63YrBEl/IPNsbp4vR1+IV+3trA1Y29s4NJOT/ozrSHMobsrbNBwwKet0660iJTuDMMMRH3OQVL9J6lMi9XangNSrxMlweLmwkKkG2W1Ju8wUbr5tnnaHW//36NPS6K/LGc4xzTRYuhvNa+rcZBq8ZJUyOetJmfZK4yw33ufPVp19osyYO8Ke17r1ZL2rspGqbM/nTXdfcxs1enmvdD5bvNEDEw3Ok42zbi9VDil6xRWEPPdKSSgf9f/tQDVNlqVTBZrr3zDfZKtVb021dNeN0rCDpE/el7aulrZ+0Hz7YduBCGKZXhbbw9IOS9oRcbsz4tYEG14Cx9g2K16/2LENBr3wcoDwWr2VaGfzsmNlGg2neu0Mulonlc6XJFnvqlRBVibBWTbkcl9L97MlKut0qrLa0+o+3e2G/Nf/Z4hqmjxl5uJlLQupuiVrElWdJC0Mk/YvsazDSy3rC2WWNb6XZd11jGXdtl/yapPre1jWD7tZ1viuThXMiDLLOqK5mqRbhunkVCl4r1UZqdLSXssxUZWHqaJJJ0UeubPF20HN43g7YzrVGel8Lj++EO42y7Qqwa+Ue673tWx8tnSrsvK53dAh6v+ppsmRyBMIM1hfbDfyQqxuaTcvDe3M2BkDzVC0JdKgoHN/vxJn4Kx4gmVSv0OkvgdJ/Q6W+h7s3K7aJJ3RfDaXDtMQL92r+cXr8pSPs+VkmQmvXaIjn2PWxc8zTC/dSHN5ZpaNNLVfqcp8ZGba89lyedZd4NULHc6Cwqz/p5omTzpkdUu6Yn80TPMKE2hUB6UhQakqKA0oid+Ww4xZsSUsbQ45txdPkc79gdRnqHONiWw10Mm0F0qi6oRcf7FTDRaX7PObgOWJJ5wfaC8DzHWEYKA9cl2VUKQHkZwHTB19uxWiUOEdkLwGI/kcv7FTSuf6MR3W+tXSwUFp/1Jp/+bgI17GY2dY2hCSNkXcfmoufhGxzO1jnAxIsgKdGf+6KymZL6D50Yq8OE689FU8sRcHSvdKhdnacZJ9fvfH33weM6x4ey817ffVJbPF64WhvC6Xb7ne19or3cuIF8t2K0TBjntAojdNYQeV/mjcJ637m7R6iTN9/EbbRqVmfI3akPRxyLk1U2X/5BfnSXZ23p5BfVKdeccO7ZyogajPDb0yPlv2+wzT78xIgTfg6zSy/QPJdisKO8iMpCfbHQE6nK1rpHcXSu/+UVq7TGoyI3pF2BGQ1jRIa5uktSGpLtz2x376dGf41kRn9OZAGu/HK1Hhm9cz7TpSXR/CfX93hK9EZwvmoJmsp0quMwi5Olv2+wzTrJcp/1TBQKLt015eskmJ9j2kV87Z/F6w3RDJ6gByPeiZnx0BfBMOW9ba5Zb1p5ssa9aJbXu03H6AZT11qWW98ZhlbVvvvbV2uq33vRZ+NlqLF/jgQBnzMpjZgAGW9cgjuRtQqhBa8xfSQFTwju3WqdGbxiO/2/61WZlUZ8LtSZWan+dNb0pvPuVM29ZG/LNE+jgg/Xu39H6Tk/nItFGn13VMt/Db29DP7+qEQhkIJ1cpv0JoiElda8fEduu06E3jUcEcn7zUE8VbJs4Vadsc+Hdtkd54VHpjrlS3qnV+l27SYWdI2/tLV/3caQcSKZ3BkfJV+IXaTbEQFMK1QDioAIhAMOKR323/bF7GiDC8XN3TDWDOPltas0Ra8bC08nkp3NhcT1sufebL0lHnSYeOcR77lRryo/D9HHEzHzpiY10AnRYNWD3yu+2fffAwZ7Pxggwzzxw0zP/dx6lsqpWmjZdW7i81bG6dX3W8NOwi6cizncvTR2Yn/OoW6kfh56qbYqHoiI11ARS9oh9nxO+OAJ7GiPDSvbVC0vFl0vAyqXuJE4iU95CO+bYThAw6uvDGiPCr8At9XIfOMPYHAKSh6IMR33uXtfdgUCbp5HInCClvXuFtYWlZg3TH49LpZxRuasjPwu/AgwN1jJQfAHjXfN304uZm7k1b0EjmpDznTQgyPRiYLXdCF+lH3aUvlDuByKaQtGCPdO8uaXmD9MzzTrreVAWlyk7EG8rdMPNNj4hcpYZ8LfxOzO/tCgBpYARWvzsCeOnh4R6o3WUOL5VGl0v9mleuLiQtqpdWNmXWlTNVt9BJk5xqjVwWCL0wsq+zN9YFUPDoTdPZDhrGxd+UvlouHd6luctuWHq5Xnq9sc1o7VG8HHzidQt1L8JWlEPSdhKFMPYHgKK1w+Nw8GRGOsJB45xznDFCnvuxFNojhSzp/xqk/6uXGjy+vpeunG524tlnnfeN9xoGZ9QdC1knAD4hGOksB41dG6XfT5Tef9FZZvBxUtUEaWe59yvSpjN6W0ENSQsA6MgYZ6Qjiu3hsWap9ORF0p5PnMHJTr1WGvkjKRjRCer6650A5qmnpFmz2t97x+/L0QMAig69aQqROeD/7X+k357lBCLlNdLnfyGNnBgdiEQGMOedl53eO4xPAQDIM4KRQtO4T3r2CukPV0tWSPpXo3TTW9LXL3SqT0zbklx25WR8CgBAnhGMFBJzQbsHv+Jc1C5sSX/aJz29V3J77JquvabXTbyAxB1AzIgNSNIZQIzxKQAAeUYwUih210kPnyl9/Lq0LyA9sscZRTWS2+3XjPsRbyCzRAOImcc33yzV16ceBC1bQQ0AAB7RtbeQApHNb0tlfaRfrJO2hjPvFRPZKydejxsv44UwPgUAIE+9aciM+G33J9LD33ACke6DpKpJqQORVA1N3Uat5eVORiS2d0yy6h6XCVQ+/NAJeubOdW5Nd14GygIAZFnRXyjP90DktyYQecsJRC5+Tnqz1ttzUzU0NdkRM4havOHdzTxT5eIO856oyqWzX0wOAFAQyIz42Wvm0bHSpjel7gOli34v9T80ew1I0xkvBAAAH5EZ8Wt01R0LnMaqXftKFz0nDfhMdANSU41iAo9416rx0oCU8UIAAB0EwUg+xDYGPbaLdHZXE11IY3/TGojE9oqJvVaNyZh4vcAZ44UAADoIgpF8XZHXzXAMLJG+VuHcf2mvtP330lklTrVLZLbDBBymPUfstWq8dql1q3tMY9V47Ubca8ykqu4BACDH6NqbS7EXnSuXdGl3qW+J9G6j9Nje9LrbZhoIGfGqe7j6LgAgh+jaWwhiG5Ge09UJRD4NOyOrptvdNl2JBkEzgQ+BCACgQFBNk0uRjUiP7yId1kVqsqQn90j7Muxum672VvcAAJBjBCO55DYi7RqQ/qO5nciL+6QN4dTdbbM5vgfjhQAAChjBSC65jUiPqXMCko0h6e+NqZ/ntVsuAACdAIOe5ZLJSNz5Y2lYF+fxwn1SnI4tGXfLBQCgEyAzkkum2qXxRakkIK0plT5KcrVcg+62AIAiRGYkl975vfThUqm0Qpr+mnOxOdNA1Ygd7j2d0VUBAOhECEZypXGv9KfrnfsjfyT1O9BplHrPPdJTT9HdFgCAZlTT5MqyWdK2tVLPKumU5myIi+62AAC0IBjJhb3bpKX3OPe/dKtU1q3tMnS3BQDARjVNLvxzntS4WxpwhHTUeTl5CwAAOguCkVz0oPn7r537J3y/bUNVAAAQhWAk29b8RfrkPamsu3TMuKy/PAAAnQ3BSLa5WRETiFT0zPrLAwDQ2RCMZNOOj6WVzzv3T/hBVl8aAIDOimAkm1Y8LFkh6YCTpYFHZvWlAQDorDIKRmbPnq2hQ4eqoqJCw4cP1/Lly5MuP2PGDB122GHq2rWrampqNHnyZO3bt0+dSqhRWvGQc3/YBGnJEumxx5zbUIph4AEAKGJpjzPy+OOPa8qUKbr//vvtQMQEGmPGjNGqVau03377tVl+7ty5uvbaa/XAAw9o5MiRevfdd3XxxRcrEAho+vTp6jRM9cyujVJpT+nMydLa2tb/mSv3zpzpDHYGAADalxkxAcQll1yiCRMm6Mgjj7SDksrKSjvYiOfVV1/VySefrO985zt2NuXLX/6yxo8fnzKb0mEbrr60JToQMWprpbFjpQULfFk1AAA6TTDS0NCgFStWaPTo0a0vUFJiP162bFnc55hsiHmOG3ysXr1aL7zwgr761a+q09iyyrkgXti0G2mIP/aIYS6SR5UNAACZV9PU1dUpFApp4MCBUfPN45UrV8Z9jsmImOedcsopsixLTU1Nuuyyy/TTn/404fvU19fbk2vHjh0qaP/4X+d2VaO0oznwiBeQrFsnLV3qXDAPAADkpzfNkiVLdMcdd+iXv/ylXn/9dS1YsEDPP/+8brvttoTPmTZtmnr16tUymUavBe29Pzu3bzWmXnbDhpyvDgAAnTYz0r9/fwWDQW3atClqvnk8aNCguM+58cYbdcEFF+gHP3DG3Tj66KO1e/duXXrppbr++uvtap5Y1113nd1INjIzUrAByfZaacs7kgLSag+9ZgYPzsdaAQDQOTMjZWVlGjZsmBYtWtQyLxwO249HjBgR9zl79uxpE3CYgMYw1TbxlJeXq2fPnlFTwVq92Lkd8jmpX1Xia9GY+SagGjUqr6sHAECnq6YxGYs5c+bo4Ycf1jvvvKPLL7/cznSY3jXGhRdeaGc2XGeeeabuu+8+zZs3T2vWrNGLL75oZ0vMfDco6dDebw7MDhntdN81YgMS9/GMGSYSy/MKAgDQycYZGTdunLZs2aKbbrpJGzdu1HHHHaeFCxe2NGpdu3ZtVCbkhhtusMcUMbe1tbUaMGCAHYjcfvvt6vDCodbMyJqwdHBf6YknpMmTpfXro8cZMYEI44wAANBGwEpUV1JATJsR05B1+/bthVVl88jPpfdvk/ZZ0t07na69JvAwg7kNGOA0VjVtREzVDBkRAECR2eHx+M21aTJlBjCbc4Nzf02TE4i4A5yNGydt3SqNH+904yUQAQAgIYKRTJiByyZOlA5qbv/xQVPr/xjgDACAtBCMZMIMXLZlvVQTJxiJHeAMAAAkRTCSCdMWZGipVBKQPglJ2xI0u2GAMwAAUiIYyYRplHpIc0ekD5IMdMYAZwAApEQwkolTTpE+U+7cfz+misZggDMAADwjGMnE9o+knpYUsqSPYjIjDHAGAEBaCEYy8cFLzm3PI6T9qqL/Z8YZmT+fAc4AAMjVCKyIGAL+pHHSlIlOrxkGOAMAICMEI+lqapA+bO6ye8jpzoBmZmAzAACQEapp0lW3SmrYJVX0kgYenVmpAwCAFgQj6dq80rnd70gp4oKAAAAgMxxN07WlORgZcFiGRQ4AACIRjGQcjByR9lMBAEBbBCPpIjMCAEBWEYyko6le2rrauT/g8OxuCQAAihTBSDrq3pOssNOTpsegnG0UAACKCcFIRlU0h7cO+w4AANqFYCTTYAQAAGQFwUg6CEYAAMg6gpF0bFnl3O5HZgQAgGwhGEmnJ80nHzj33/9UeuwxackSKRTK2sYAAKAYcaE8r0wgYoWkBklnjG2dX10tzZwpnXtubrYQAACdHJkRr55/2Lnd1BQ9v7ZWGjtWWrAgy5sGAIDiQDDihamKeeYB5/6WcPT/LMu5nTSJKhsAADJAMOLF0qVS+e74wYgbkKxb5ywHAADSQjDixYYN0n7NRbUllHw5AACQFoIRLwb2l/o2F9XmOJkR1+DB6ZU+AAAgGPHkiMFSMCDVW9LO5jYikczQ8DU10qhR7FIAAKSJzIgXW99rbS8Se00a9/GMGVIwmG75AwBQ9AhG0hl59ehTpaqq6P+ZcUbmz2ecEQAAMsSgZ15sfse5PWGM9OGzTq8Z01jVtBExVTNkRAAAyBjBSDqZkQFHOIHHqadmXuIAACAK1TSphBqlT9537g84LOXiAAAgPQQjqWxdLYUbpbLuUq/qNIsXAACkQjCSypaVrVmR2J40AACg3QhGUtnsBiOHt7+0AQBAGwQjqdS969zSXgQAgJwgGEll1ybntmfM+CIAACArCEZS2fOJc1vZLzslDgAAohCMpLK7zrnt1j/logAAIH0EI8mEwxGZEYIRAABygWAkmX3bJCvk3KeaBgCAnCAY8VJFU9FLKi3LzRYAAKDIEYwks6c5GKGKBgCAnCEYSWbnZud2jyUtWSKFmqtsAABA1hCMJLJggTT5P537b6ySTjtNGjrUmQ8AALKGYCQeE3CMHSs1bGvNjBi1tc58AhIAALKGYCSWqYqZOFGyLKmy+cJ4u5uDETPPmDSJKhsAALKEYCTW0qXS+vXO/cqS6GDEDUjWrXOWAwAA7UYwEmvDhtb73ZozI3vCyZcDAAAZIxiJNXhw22AkMjMSbzkAAJAxgpFYo0ZJ1dVSINDaZsRtwGqY+TU1znIAAKDdCEZiBYPSzJnO/dgGrCYQMWbMcJYDAADtRjASz7nnSvMeloIxmRGTMZk/3/k/AADwLxiZPXu2hg4dqoqKCg0fPlzLly9Puvy2bdt0xRVXaPDgwSovL9dnPvMZvfDCCypo/3GScxuslP53rrR4sbRmDYEIAABZVpruEx5//HFNmTJF999/vx2IzJgxQ2PGjNGqVau03377tVm+oaFBX/rSl+z/zZ8/X1VVVfroo4/Uu3dvdYiL5PUcKI0f7/faAADQaaUdjEyfPl2XXHKJJkyYYD82Qcnzzz+vBx54QNdee22b5c38rVu36tVXX1WXLl3seSar0mEuktdtgN9rAgBAp5ZWNY3JcqxYsUKjR49ufYGSEvvxsmXL4j7nd7/7nUaMGGFX0wwcOFBHHXWU7rjjDoUK/aJzbmakW3+/1wQAgE4trcxIXV2dHUSYoCKSebxy5cq4z1m9erVeeuklnX/++XY7kffff18//OEP1djYqKlTp8Z9Tn19vT25duzYId+Ckcp++X9vAACKSM5704TDYbu9yK9+9SsNGzZM48aN0/XXX29X7yQybdo09erVq2WqMeN6+FZNQ2YEAICCCUb69++vYDCoTZs2Rc03jwcNGhT3OaYHjek9Y57nOuKII7Rx40a72iee6667Ttu3b2+Z1plrwfiWGSEYAQCgYIKRsrIyO7uxaNGiqMyHeWzahcRz8skn21UzZjnXu+++awcp5vXiMd1/e/bsGTXlHQ1YAQAozGoa0613zpw5evjhh/XOO+/o8ssv1+7du1t611x44YV2ZsNl/m9600ycONEOQkzPG9OA1TRoLWi7P3Fuu9FmBACAguraa9p8bNmyRTfddJNd1XLcccdp4cKFLY1a165da/ewcZn2Hn/84x81efJkHXPMMfY4IyYwueaaa1TQdm9xbqmmAQAgpwKWZcW5JG1hMb1pTENW034kL1U2pkhuGyCFG6XJb0m9qnP/ngAAdDJej99cmyaefdudQMQgMwIAQE4RjMSzp7m9SFkPqUtFbrcAAABFjmAkWXsRGq8CAJBzBCPxMMYIAAB5QzASD6OvAgCQNwQj8ZAZAQAgbwhGkjVg5bo0AADkHMFI0gasXJcGAIBcIxiJh2oaAADyhmAkHhqwAgCQNwQjyS6SV8lF8gAAyDWCkXjXpWlpMzIg5xsAAIBiRzASq35H63VpaMAKAEDOEYwkarzapZvUpWvutwAAAEWOYCThGCO0FwEAIB8IRmLRXgQAgLwiGInFGCMAAOQVwUgsxhgBACCvCEZiMcYIAAB5RTASi8wIAAB5RTASiwasAADkFcFILBqwAgCQVwQjsRhnBACAvCIYaXNdmuYRWCv753dLAABQpAhGItXvlEL1zn2uSwMAQF4QjMTrSdOlUirrlp8tAABAkSMYibTnU+e2kuvSAACQLwQjkRr3OLdcrRcAgLwhGInkthcJludvCwAAUOQIRiI1NTi3pWX+bA0AAIoQwUgkMiMAAOQdwUgkMiMAAOQdwUgkMiMAAOQdwUikpuYGrLQZAQAgbwhGIoWaG7DSmwYAgLwhGImbGanI3xYAAKDIEYzEy4xQTQMAQN4QjMTLjFBNAwBA3hCMRCIzAgBA3hGMRGra59ySGQEAIG8IRiLRtRcAgLwjGIlE114AAPKOYCRuZoSr9gIAkC8EI3EzI1y1FwCAfCEYiURmBACAvCMYiURmBACAvCMYiURmBACAvCMYiRRiBFYAAPKNYCRSE9emAQAg3whG4mVGuGovAAB5QzASLzNC114AAPKGYCReZuTFl6QlS6RQKH9bAgCAIkUw4lqwQNq6xbn//66RTjtNGjrUmQ8AAHKGYMQwAcfYsVLQckol1HxbW+vMJyABACBnCEZMVczEiZJlSaUBp1SamkvHzDMmTaLKBgCAQgpGZs+eraFDh6qiokLDhw/X8uXLPT1v3rx5CgQCOvvss1Uwli6V1q+PLgk3M+IGJOvWOcsBAAD/g5HHH39cU6ZM0dSpU/X666/r2GOP1ZgxY7R58+akz/vwww/14x//WKNGjVJB2bDBuS2NmNeUZDkAAOBvMDJ9+nRdcsklmjBhgo488kjdf//9qqys1AMPPJDwOaFQSOeff75uueUWHXTQQSoogwc7t8HmKhojlGQ5AADgXzDS0NCgFStWaPTo0a0vUFJiP162bFnC5916663ab7/99P3vf18Fx2RqqqulLs3BSNiSImppFAhINTXOcgAAIOsiKydSqqurs7McAwcOjJpvHq9cuTLuc1555RX95je/0RtvvOH5ferr6+3JtWPHDuVMMCjNnCn94Jttq2hMIGLMmOEsBwAAOlZvmp07d+qCCy7QnDlz1L9/f8/PmzZtmnr16tUy1ZjMRC6de640a2bbKhqTMZk/3/k/AADwPzNiAopgMKhNmzZFzTePBw0a1Gb5Dz74wG64euaZZ7bMC4fDzhuXlmrVqlU6+OCD2zzvuuuusxvJRmZGch6QnPYF6V1JvfpKc//HaSNiqmbIiAAAUDjBSFlZmYYNG6ZFixa1dM81wYV5fOWVV7ZZ/vDDD9e///3vqHk33HCDnTGZOXNmwgCjvLzcnvIq1Hxdmq49pPHj8/veAAAUsbSCEcNkLC666CIdf/zxOvHEEzVjxgzt3r3b7l1jXHjhhaqqqrKrWsw4JEcddVTU83v37m3fxs73XZN7xd48B0EAABS5tIORcePGacuWLbrpppu0ceNGHXfccVq4cGFLo9a1a9faPWw67EXyCEYAAMirgGW5Y54XLtNmxDRk3b59u3r27JmbN1m1UHpsnDTk89Kli3PzHgAAFJEdHo/fHTCFkSNkRgAA8AXBiKupuQFrsMyfLQEAQJEiGHE17XNuaTMCAEBeEYzEVtOQGQEAIK8IRmKraciMAACQVwQjbTIjjDMCAEA+EYy0yYzQgBUAgHwiGHGRGQEAwBcEI22GgyczAgBAPhGMxF4ojzYjAADkFcGIiwvlAQDgC4KR2MwIXXsBAMgrgpHYzAjVNAAA5BXBSJvMCA1YAQDIJ4IRF5kRAAB8QTASO84IbUYAAMgrgpHYEVi5UB4AAHlFMOJq2ufckhkBACCvCEbaDHpGA1YAAPKJYMTFoGcAAPiCYMTFcPAAAPiCYMTFhfIAAPAFwUhs115GYAUAIK8IRmK79jICKwAAeUUw4iIzAgCALwhGjFCTZIWdEmGcEQAA8opgJDIrYhCMAACQVwQjkT1pDBqwAgCQVwQjkWOMBEqkYGl+twAAAEWOYCQyM0JWBACAvCMYicyM0K0XAIC8IxiJvGIvmREAAPKOYCRqwLPy/G8BAACKHMFI1IBnZf5uDQAAihDBSNRF8siMAACQbwQjkQ1YyYwAAJB3BCMGmREAAHxDMGKQGQEAwDcEIwaZEQAAfEMwEtmbprTCvy0BAECRIhiJHGeEBqwAAOQdwUhUZoSuvQAA5BvBiEFmBAAA3xCMGGRGAADwDcFIZG8a2owAAJB3BCOR44zQZgQAgLwjGDGa9jmlEaQBKwAA+UYwEtmAtZSr9gIAkG8EI5ENWMmMAACQdwQjUcPBkxkBACDfCEaiLpRHmxEAAPKNYMTgQnkAAPiGYCQqM0I1DQAA+UYwEpUZ4aq9AADkG8FI1KBnZEYAAOgQwcjs2bM1dOhQVVRUaPjw4Vq+fHnCZefMmaNRo0apT58+9jR69Oiky/s7HDwNWAEAKPhg5PHHH9eUKVM0depUvf766zr22GM1ZswYbd68Oe7yS5Ys0fjx47V48WItW7ZMNTU1+vKXv6za2loVDC6UBwCAbwKWZVnpPMFkQk444QTNmjXLfhwOh+0A46qrrtK1116b8vmhUMjOkJjnX3jhhZ7ec8eOHerVq5e2b9+unj17Kut+fpi0a6P0n0ulwcdk//UBAChCOzwev9PKjDQ0NGjFihV2VUvLC5SU2I9N1sOLPXv2qLGxUX379lXBIDMCAIBvStNZuK6uzs5sDBw4MGq+ebxy5UpPr3HNNddoyJAhUQFNrPr6enuKjKzycm0auvYCANC5e9Pceeedmjdvnp5++mm78Wsi06ZNs9M67mSqgfJy1d5SGrACAFDQwUj//v0VDAa1adOmqPnm8aBBg5I+9+c//7kdjPzpT3/SMcckb5dx3XXX2fVL7rRu3TrlTDgkWSHnPr1pAAAo7GCkrKxMw4YN06JFi1rmmQas5vGIESMSPu+uu+7SbbfdpoULF+r4449P+T7l5eV2Q5fIKefdeg3GGQEAoLDbjBimW+9FF11kBxUnnniiZsyYod27d2vChAn2/00PmaqqKruqxfjZz36mm266SXPnzrXHJtm4caM9v3v37vZUMI1XDTIjAAAUfjAybtw4bdmyxQ4wTGBx3HHH2RkPt1Hr2rVr7R42rvvuu8/uhTN27Nio1zHjlNx8883yndt41Qh28XNNAAAoSmmPM+KHnI4zsm2tNONoJytyY/yB2wAAQIGMM9IpuZkRetIAAOALghEGPAMAwFcEI1wkDwAAXxGMhNxqmjJ/twQAAEWKYITMCAAAviIYITMCAICvCEbIjAAA4CuCEXrTAADgK4IRd5yRIA1YAQDwA8FI0z6nJBj0DAAAXxCMuA1YyYwAAOALghG3ASuZEQAAfEEw4jZgJTMCAIAvCEa4UB4AAL4iGGnJjJT7uyUAAChSBCNkRgAA8BXBCIOeAQDgK4IRBj0DAMBXBCNkRgAA8BXBSMuF8hgOHgAAPxCMuCOwMugZAAC+IBhpyYzQtRcAAD8QjLRkRqimAQDADwQjZEYAAPAVwUjLhfLIjAAA4AeCEYaDBwDAVwQjLZkRGrACAOAHghG3ASvjjAAA4AuCETIjAAD4imCEQc8AAPAVwQhdewEA8FVxByPhsBRudO7TgBUAAF8UdzDiVtEYNGAFAMAXRR6MNHfrNciMAADgi+IORprIjAAA4LfiDkZaRl8tkwIBv9cGAICiVNzBCD1pAADwXXEHIy1jjHCRPAAA/FLcwUjTPuc2yHVpAADwS5EHI2RGAADwW3EHIy0NWMmMAADgl+IORsiMAADgu+IORsiMAADgu+IORtyuvYy+CgCAb4o7GGnp2kubEQAA/FLcwQiDngEA4LviDkYY9AwAAN8VdzBCZgQAAN8VdzDi9qZhOHgAAHxT3MGIO84Ig54BAOCb4g5GWjIj9KYBAMAvxR2MtGRGuGovAAB+Ke5ghMwIAAC+K+5gpGmfc0tmBAAA3xRvMBIKSbXrnPsfrXceAwCAjhGMzJ49W0OHDlVFRYWGDx+u5cuXJ13+ySef1OGHH24vf/TRR+uFF16QrxYskIYOlRb/2Xl87y+dx2Y+AAAo7GDk8ccf15QpUzR16lS9/vrrOvbYYzVmzBht3rw57vKvvvqqxo8fr+9///v6xz/+obPPPtue3nzzTfnCBBxjx0rr10ulzfNMUqS21plPQAIAQF4FLMuy0nmCyYSccMIJmjVrlv04HA6rpqZGV111la699to2y48bN067d+/Wc8891zLvpJNO0nHHHaf777/f03vu2LFDvXr10vbt29WzZ09lzFTFmAyICUSM8yulQ0qlp/dK/2qUAgGpulpas0YKBjN/HwAAIK/H77QyIw0NDVqxYoVGjx7d+gIlJfbjZcuWxX2OmR+5vGEyKYmWN+rr6+0PEDllxdKlrYGI4WZGmprjMROXrVvnLAcAAPIirWCkrq5OoVBIAwcOjJpvHm/cuDHuc8z8dJY3pk2bZkdS7mQyL1mxYUP0Yzf5EUqxHAAAKK7eNNddd52d0nGndSZbkQ2DB0c//mej9Eq9VBdOvhwAAMgZt6LCk/79+ysYDGrTpk1R883jQYMGxX2OmZ/O8kZ5ebk9Zd2oUU6bENNY1VTJrGiM/r/bZsQsBwAACi8zUlZWpmHDhmnRokUt80wDVvN4xIgRcZ9j5kcub7z44osJl88p0yh15szWwCOS+3jGDBqvAgBQyNU0plvvnDlz9PDDD+udd97R5ZdfbveWmTBhgv3/Cy+80K5mcU2cOFELFy7UL37xC61cuVI333yzXnvtNV155ZXyxbnnSvPnS1VV0fNNRsTMN/8HAACFWU3jdtXdsmWLbrrpJrsRqumia4INt5Hq2rVr7R42rpEjR2ru3Lm64YYb9NOf/lSHHnqonnnmGR111FHyjQk4zjrL6TVjGquaNiKmaobuvAAAFP44I37I2jgjAACgY48zAgAAkG0EIwAAwFcEIwAAwFcEIwAAwFcEIwAAwFcEIwAAwFcEIwAAwFcEIwAAwFcEIwAAoGMNB+8Hd5BYM5IbAADoGNzjdqrB3jtEMLJz5077tqamxu9VAQAAGRzHzbDwHfraNOFwWB9//LF69OihQCDQrgjNBDTr1q3jGjc5RlnnD2VNWXdG7Nedo6xNiGECkSFDhkRdRLdDZkbMB6iurs7a65nC5oJ7+UFZ5w9lTVl3RuzXHb+sk2VEXDRgBQAAviIYAQAAviqqYKS8vFxTp061b0FZdxbs15R1Z8R+XVxl3SEasAIAgM6rqDIjAACg8BCMAAAAXxGMAAAAXxGMAAAAXxVNMDJ79mwNHTpUFRUVGj58uJYvX+73KnV406ZN0wknnGCPjLvffvvp7LPP1qpVq6KW2bdvn6644gr169dP3bt313nnnadNmzb5ts6dxZ133mmPRjxp0qSWeZR19tTW1uq73/2uvd927dpVRx99tF577bWW/5t2/zfddJMGDx5s/3/06NF67733srgGxSEUCunGG2/UgQceaJfjwQcfrNtuuy3qOiaUdeb+8pe/6Mwzz7RHPzW/F88880zU/72U7datW3X++efbg6H17t1b3//+97Vr1y5lnVUE5s2bZ5WVlVkPPPCA9dZbb1mXXHKJ1bt3b2vTpk1+r1qHNmbMGOvBBx+03nzzTeuNN96wvvrVr1r777+/tWvXrpZlLrvsMqumpsZatGiR9dprr1knnXSSNXLkSF/Xu6Nbvny5NXToUOuYY46xJk6c2DKfss6OrVu3WgcccIB18cUXW3/729+s1atXW3/84x+t999/v2WZO++80+rVq5f1zDPPWP/85z+tb3zjG9aBBx5o7d27N0trURxuv/12q1+/ftZzzz1nrVmzxnryySet7t27WzNnzmxZhrLO3AsvvGBdf/311oIFC0x0Zz399NNR//dStmeccYZ17LHHWn/961+tpUuXWocccog1fvx4K9uKIhg58cQTrSuuuKLlcSgUsoYMGWJNmzbN1/XqbDZv3mzv8C+//LL9eNu2bVaXLl3sHxjXO++8Yy+zbNkyH9e049q5c6d16KGHWi+++KL1xS9+sSUYoayz55prrrFOOeWUhP8Ph8PWoEGDrLvvvrtlnin/8vJy67HHHsvimnR+X/va16zvfe97UfPOPfdc6/zzz7fvU9bZExuMeCnbt99+237e3//+95Zl/vCHP1iBQMCqra3N4tpZVqevpmloaNCKFSvs9FPktW7M42XLlvm6bp3N9u3b7du+ffvat6bcGxsbo8r+8MMP1/7770/ZZ8hUeX3ta1+LKlPKOrt+97vf6fjjj9c3v/lNu/rxc5/7nObMmdPy/zVr1mjjxo1R28Bce8NU//Kbkp6RI0dq0aJFevfdd+3H//znP/XKK6/oK1/5CmWdY172Y3NrqmbM98FlljfH0L/97W9ZXZ8OcaG89qirq7PrJQcOHBg13zxeuXKlb+vV2ZgrK5v2CyeffLKOOuooe57Z0cvKyuydObbszf+Qnnnz5un111/X3//+9zb/o6yzZ/Xq1brvvvs0ZcoU/fSnP7XL+0c/+pG9L1900UUt+2683xT26/Rce+219hVjzUlKMBi0f6tvv/12u42CQVnnjpeyNbcmII9UWlpqn3Bme1/v9MEI8nfG/uabb9pnNcg+c2nviRMn6sUXX7QbYSO3gbU5E7zjjjvsxyYzYvbt+++/3w5GkD1PPPGEHn30Uc2dO1ef/exn9cYbb9gnNabBJWVdXDp9NU3//v3tiDu2B4d5PGjQIN/WqzO58sor9dxzz2nx4sWqrq5umW/K11STbdu2LWp5yj59pspr8+bN+vznP2+fmZjp5Zdf1n//93/b983ZDGWdHaZnwZFHHhk174gjjtDatWvt++7vBr8p7feTn/zEzo58+9vftnssXXDBBZo8ebLdU4+yzi0v+7G5Nb87kZqamuweNtk+fnb6YMSkVocNG2bXS0ae+ZjHI0aM8HXdOjrTJsoEIk8//bReeuklu3teJFPuXbp0iSp70/XX/KhT9uk5/fTT9e9//9s+c3Qnc/Zu0tnufco6O0xVY2wXddOm4YADDrDvm/3c/BBH7temqsHUobNfp2fPnj12+4NI5uTR/EZT1rnlZT82t+Zk0pwMucxvvdk+pm1JVllF0rXXtBB+6KGH7NbBl156qd21d+PGjX6vWod2+eWX293ClixZYm3YsKFl2rNnT1R3U9Pd96WXXrK79o4YMcKe0H6RvWko6+x2nS4tLbW7nb733nvWo48+alVWVlqPPPJIVJdI8xvy7LPPWv/617+ss846i669Gbjooousqqqqlq69pgtq//79rauvvpqyzlLvu3/84x/2ZA7306dPt+9/9NFHnvdj07X3c5/7nN3N/ZVXXrF789G1tx3uvfde+6BoxhsxXX1Nn2m0j9m5401m7BGX2al/+MMfWn369LF/0M855xw7YEH2gxHKOnt+//vfW0cddZR9EnP44Ydbv/rVr6L+b7pF3njjjdbAgQPtZU4//XRr1apVWVyD4rBjxw57Hza/zRUVFdZBBx1kj4tRX1/fsgxlnbnFixfH/Y02QaDXsv3kk0/s4MOM/9KzZ09rwoQJdpCTbQHzJ7u5FgAAAO86fZsRAABQ2AhGAACArwhGAACArwhGAACArwhGAACArwhGAACArwhGAACArwhGAACArwhGAACArwhGAACArwhGAACArwhGAACA/PT/ASG86LhKcn0+AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 100 # taille maximale de l'échantillon\n",
    "repet = 1000 # nombre d'échantillons aléatoires utilisés pour chaque taille\n",
    "# d'échantillon\n",
    "# Tableaux qui vont accueillir ...\n",
    "# ... les moyennes empiriques pour chaque taille d'échantillon (de 1 à n)\n",
    "moy_emps = zeros(n)\n",
    "# ... les variances empiriques pour chaque taille d'échantillon (de 1 à n)\n",
    "var_emps = zeros(n)\n",
    "# Pour chaque taille d'échantillon ...\n",
    "for i in range(1, n+1):\n",
    "    # Somme des moyennes et variances de la variable population des\n",
    "    # 1000 échantillons de taille i, initialisées à zéros\n",
    "    acc_moy_echs = 0\n",
    "    acc_var_echs = 0\n",
    "    # ... on étudie 1000 échantillons\n",
    "    for _ in range(repet):\n",
    "        # Choix d'un échantillon aléatoire de n = i valeurs de population\n",
    "        pop2_ech = choices(POP2, k=i)\n",
    "        # Incrémentation des variables d'accumulation\n",
    "        acc_moy_echs += mean(pop2_ech)\n",
    "        acc_var_echs += var(pop2_ech)\n",
    "\n",
    "    # calcul des moyennes et variances empiriques sur 1000 échantillons de\n",
    "    # même taille i :\n",
    "    moy_emp = acc_moy_echs / repet\n",
    "    var_emp = acc_var_echs / repet\n",
    "\n",
    "    # ajout des moyennes et variances empiriques dans les tableaux\n",
    "    # attention : les tailles d'échantillon vont de 1 à n mais les indices des\n",
    "    # tableaux vont de 0 à n - 1 ce qui justifie le i-1 en indiçage.\n",
    "    moy_emps[i-1] = moy_emp \n",
    "    var_emps[i-1] = var_emp\n",
    "\n",
    "# calcul des ratios (la division sur ndarray divise chaque case). On fait la\n",
    "# division à la fin sur toute la ndarray pour être efficace.\n",
    "ratios_moy = moy_emps / moy_glob\n",
    "ratios_var = var_emps / var_glob\n",
    "\n",
    "x = arange(1, n+1) # ndarray des entiers de 1 à n (les tailles d'échantillons)\n",
    "# Nuages de points : ratios en fonction de la taille d'échantillon\n",
    "scatter(x, ratios_moy, color='b')\n",
    "scatter(x, ratios_var, color='r')\n",
    "# Ajout des courbes de convergence théorique sur le graphique\n",
    "plot(x, ones(n)) # ones(n) est une ndarray ne contenant que des 1.\n",
    "plot(x, (x-1)/x)\n",
    "show()\n",
    "\n",
    "# Commentaire. On voit sans surprise que la moyenne empirique (respectivement\n",
    "# la variance empirique) converge vers la moyenne gobale (respectivement la\n",
    "# variance globale) lorsque la taille de l'échantillon augmente. À noter que la\n",
    "# variance empirique converge moins vite que la moyenne empirique.\n"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "iut",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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 },
 "nbformat": 4,
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}