{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Données"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([14. ,  7.6, 11.2, 12.8, 12.5,  9.9, 14.9,  9.4, 16.9, 10.2, 14.9,\n",
       "       18.1,  7.3,  9.8, 10.9, 12.2,  9.9,  2.9,  2.8, 15.4, 15.7,  9.7,\n",
       "       13.1, 13.2, 12.3, 11.7, 16. , 12.4, 17.9, 12.2, 16.2, 18.7,  8.9,\n",
       "       11.9, 12.1, 14.6, 12.1,  4.7,  3.9, 16.9, 16.8, 11.3, 14.4, 15.7,\n",
       "       14. , 13.6, 18. , 13.6, 19.9, 13.7, 17. , 20.5,  9.9, 12.5, 13.2,\n",
       "       16.1, 13.5,  6.3,  6.4, 17.6, 19.1, 12.8, 15.5, 16.3, 15.2, 14.6,\n",
       "       19.1, 14.4, 21.4, 15.1, 19.6, 21.7, 11.3, 15. , 14.3, 16.8, 14. ,\n",
       "        6.8,  8.2, 19.9, 20.4, 14.6, 16.4, 18.7, 16.8, 15.8, 20.4, 15.8,\n",
       "       22.4, 16.2, 20.3, 23.4, 12.1, 15.5, 15.4, 18.4, 15.7, 10.2,  8.9,\n",
       "       21. ])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "L = np.array([14.0, 7.6, 11.2, 12.8, 12.5, 9.9, 14.9, 9.4, 16.9, 10.2, 14.9, 18.1, 7.3, 9.8,\n",
    "              10.9,12.2, 9.9, 2.9, 2.8, 15.4, 15.7, 9.7, 13.1, 13.2, 12.3, 11.7, 16.0, 12.4,\n",
    "              17.9, 12.2, 16.2, 18.7, 8.9, 11.9, 12.1, 14.6, 12.1, 4.7, 3.9, 16.9, 16.8,\n",
    "              11.3, 14.4, 15.7, 14.0, 13.6, 18.0, 13.6, 19.9, 13.7, 17.0, 20.5, 9.9, 12.5,\n",
    "              13.2, 16.1, 13.5, 6.3, 6.4, 17.6, 19.1, 12.8, 15.5, 16.3, 15.2, 14.6, 19.1,\n",
    "              14.4, 21.4, 15.1, 19.6, 21.7, 11.3, 15.0, 14.3, 16.8, 14.0, 6.8, 8.2, 19.9,\n",
    "              20.4, 14.6, 16.4, 18.7, 16.8, 15.8, 20.4, 15.8, 22.4, 16.2, 20.3, 23.4, 12.1,\n",
    "              15.5, 15.4, 18.4, 15.7, 10.2, 8.9, 21.0])\n",
    "L"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Extrema\n",
    "\n",
    "## Minimum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.8"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.min(L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.8"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "min = L[0]\n",
    "\n",
    "for i in range(1, len(L)):\n",
    "    if L[i] < min:\n",
    "        min = L[i]\n",
    "\n",
    "min        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Maximum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "23.4"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "23.4"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max = L[0]\n",
    "\n",
    "for i in range(1, len(L)):\n",
    "    if L[i] > max:\n",
    "        max = L[i]\n",
    "\n",
    "max"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Médiane"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14.5"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(L)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Moyenne\n",
    "\n",
    "## Calcul de la moyenne avec la fonction *mean* de *numpy*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14.113000000000001"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean = np.mean(L)\n",
    "mean"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calcul de la moyenne *à la main*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14.113000000000001"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean2 = np.sum(L)/len(L)\n",
    "mean2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparaison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean == mean2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Écart-type\n",
    "\n",
    "## Calcul de l'écart-type (corrigé) avec la fonction *std* de *numpy*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.334094455301447"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SD = np.std(L, ddof=1)\n",
    "SD"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calcul de l'écart-type *à la main*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.3340944553014475"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from math import *\n",
    "\n",
    "V = 0\n",
    "\n",
    "for i in range(len(L)):\n",
    "    V += (L[i]-mean2)**2\n",
    "\n",
    "V /= len(L)-1\n",
    "\n",
    "SD2 = sqrt(V)\n",
    "SD2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparaison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SD == SD2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-8.881784197001252e-16"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SD - SD2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bien que les deux résultats ne soient pas **strictement** égaux, la différence est particulièrement faible (correspondant peut-être à la précision machine)."
   ]
  }
 ],
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  "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",
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