Term_Moyenne_et_incertitude_type_ELEVE.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Term_Moyenne et incertitude type_ELEVE.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "L3_sxmiYvpBg",
        "colab_type": "text"
      },
      "source": [
        "# Détermination de l'incertitude de mesure : Calcul de la Moyenne et de l'incertitude type de valeurs expérimentales\n",
        "https://docs.scipy.org/doc/scipy/reference/stats.html\n",
        "https://vigon.pages.math.unistra.fr/-/aleaDataSignal/-/jobs/11233/artifacts/public/alea/04-plusDeLois.html\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zKmPuGgoyeGj",
        "colab_type": "text"
      },
      "source": [
        "**1ère METHODE en utilisant les relation de moyenne et d'écart**\n",
        "-   Remplacer ces valeurs par celles obtenues par les groupes\n",
        "-   Modifier les Paramètres du graphiques\n",
        "-   Compléter les lignes incomplètes\n",
        "-   Arrondir les valeurs  à 3 chiffres après la virgule"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ybn7EbGCvn_G",
        "colab_type": "code",
        "outputId": "2c1de8d2-abca-453b-f284-04a79e061a85",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 389
        }
      },
      "source": [
        "import numpy as np\n",
        "from scipy.stats import *\n",
        "from math import*\n",
        "import numpy as np\n",
        "from scipy import *\n",
        "import scipy.stats  as stats\n",
        "import statistics\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Valeurs de volume de solution titrante versée à l'équivalence obtenu par différents groupes\n",
        "valeurs =[24.1 ,25,26,25.4,23,25]\n",
        "\n",
        "# Calcul de la moyenne\n",
        "moy=np.mean(valeurs)\n",
        "# Calcul de l'écart type\n",
        "etype=np.std(valeurs)\n",
        "# Calcul de l'effectif\n",
        "effectif=len(valeurs)\n",
        "# Calcul de l'incertitude type\n",
        "itype=etype/np.sqrt(effectif)\n",
        "# Affichage des données statistiques\n",
        "print(\"Les valeurs obtenues par les groupes sont : \",.........)\n",
        "print('La moyenne des valeurs étudiées est', .........)\n",
        "print('L effectif des valeurs étudiées est', ......)\n",
        "print('L écart_type des valeurs étudiées est', round(..........,2))\n",
        "print(\"L'incertitude des valeurs étudiées est\",round(..........,2))\n",
        "\n",
        "plt.hist(valeurs,bins=20,range=(22,26),align=\"right\",rwidth=0.9,color=\"b\",label=\"V titrant\")\n",
        "plt.title(\"volume de solution titrante versée à l'équivalence\")\n",
        "plt.xlabel(\"Volume (mL)\")\n",
        "plt.ylabel(\"Fréquence\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Les valeurs obtnues par lesgroupes sont :  [24.1, 25, 26, 25.4, 23, 25]\n",
            "La moyenne des valeurs étudiées est 24.75\n",
            "L effectif des valeurs étudiées est 6\n",
            "L écart_type des valeurs étudiées est 0.97\n",
            "L'incertitude des valeurs étudiées est 0.39\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "cLkbeJqMyruZ"
      },
      "source": [
        "**2ème METHODE à analyser en utilisant la bibliothèque SCIPY de Python** \n",
        "\n",
        "https://code.tutsplus.com/fr/tutorials/mathematical-modules-in-python-statistics--cms-27750 "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TarJ8zXIRPNy",
        "colab_type": "code",
        "outputId": "c3182c91-aa79-44ac-beeb-f553cdce0037",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 378
        }
      },
      "source": [
        "from math import*\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "from scipy import *\n",
        "import numpy as np\n",
        "import scipy.stats  as stats\n",
        "import statistics\n",
        "\n",
        "# Valeurs de capacités mesurées\n",
        "valeurs=[24.1 ,25,26,25.4,23.5,25]\n",
        "essai=[1,2,3,4,5,6]\n",
        "plt.plot(essai,valeurs,'o', c='b',linestyle = 'dashed',label='Points issus de mesure du dipole 1')\n",
        "\n",
        "#Moyenne avec Numpy\n",
        "m = np.mean(valeurs)\n",
        "\n",
        "#Moyenne avec Statistics\n",
        "p=statistics.mean([24,25,25.2,27,28,23,25])\n",
        "\n",
        "#La fonction mode() renvoie le point de données le plus courant à partir de données numériques discrètes \n",
        "mode=statistics.mode(valeurs)\n",
        "\n",
        "#la valeur médiane des données numériques données en calculant la moyenne de deux points intermédiaires si nécessaire. \n",
        "#Si le nombre de points de données est impair, il renvoie le point central. \n",
        "#Si le nombre de points de données est pair, il renvoie la moyenne de deux valeurs médianes.\n",
        "ml=statistics.median_low(valeurs)\n",
        "mh=statistics.median_high(valeurs)\n",
        "\n",
        "#ecart tytpe (sigma) qui mesure de dispersion de données. Écart-type = σ= √ [(Σ((X-μ)2))/(N)]\n",
        "sigma = np.std(valeurs,ddof=1)\n",
        "\n",
        "print(\"La valeur moyenne est de\",round(m,2))\n",
        "print(\"La valeur moyenne 2 est de\",round(p,2))\n",
        "print(\"La médiane Haute est de\",round(mh,2))\n",
        "print(\"La médiane Basse est de\",round(ml,2))\n",
        "print(\"le point de données le plus fréquent est de\",mode)\n",
        "print(\"L'écart-type est de\",round(sigma,3))\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "La valeur moyenne est de 24.83\n",
            "La valeur moyenne 2 est de 25.31\n",
            "La médiane Haute est de 25\n",
            "La médiane Basse est de 25\n",
            "le point de données le plus fréquent est de 25\n",
            "L'écart-type est de 0.9\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}