{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Histogrammes, étude statistique et incertitude-type de répétabilité\n", "\n", "**Comment tracer un histogramme, réaliser une étude statistique et calculer une incertitude-type de répétabilité (type A) sous Python?**\n", "\n", "code sous licence creative commun CC BY-NC-SA BY Gaëlle Rebolini" ] }, { "cell_type": "raw", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ ":download:`Télécharger le pdf <./13-histogramme.pdf>`\n", "\n", ":download:`Télécharger le notebook <./13-histogramme.ipynb>`\n", "\n", ":download:`Lancer le notebook sur binder (lent) `" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ceci est un petit tutoriel permettant de tracer des histogrammes, de déterminer une valeur moyenne, un écart-type et une incertitude-type de répétabilité (type A) à partir d'un échantillon de valeurs. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Voici un programme exploitant des mesures de volume réalisées à l'éprouvette graduée. On mesure le plus précisément possible 50 mL d'eau à l'aide d'une éprouvette graduée. Puis, on pèse cette eau et on en déduit par un simple calcul faisant intervenir la masse volumique, le volume d'eau correspondant avec une meilleure précision. On réalise la manipulation un grand nombre de fois, ce qui nous permet d'obtenir un échantillon de valeurs.\n", "\n", "Dans un premier temps, vous est présenté le programme complet. Les lignes de code seront explicitées dans un second temps." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Le volume moyen : 49.506249999999994 mL\n", "L'écart-type vaut : 0.8814042418209694 mL\n", "Le nombre de mesures vaut : 16\n", "L'incertitude-type de répétabilité de deltat vaut : 0.22035106045524236 mL\n" ] } ], "source": [ "import numpy as np \n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "Veprouvette =[49.61,49.55,50.91,50.87,48.03,50.29,48.58,48.06,50.06,50.72,48.95,49.4,49.21,49.31,49.78,48.77]\n", "plt.figure(figsize=(12,10))\n", "plt.hist(Veprouvette,bins=20,range=(45,55),align=\"mid\",rwidth=0.9,color=\"b\",edgecolor=\"red\",label=\"éprouvette\")\n", "plt.title(\"Volume d'eau contenu par une éprouvette graduée pour 50mL mesuré\")\n", "plt.xlabel(\"Volume (mL)\")\n", "plt.ylabel(\"Fréquence\")\n", "plt.legend()\n", "plt.show()\n", "\n", "\n", "Vmoy=np.mean(Veprouvette)\n", "ecarttype=np.std(Veprouvette)\n", "effectif=len(Veprouvette)\n", "incertitudetype=ecarttype/np.sqrt(effectif)\n", "print(\"{0:55}\".format(\"Le volume moyen :\"),Vmoy,\"mL\")\n", "print(\"{0:55}\".format(\"L'écart-type vaut :\"),ecarttype,\"mL\")\n", "print(\"{0:55}\".format(\"Le nombre de mesures vaut :\"),effectif)\n", "print(\"{0:55}\".format(\"L'incertitude-type de répétabilité de deltat vaut :\"),incertitudetype,\"mL\")\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## EXPLICATIONS DU PROGRAMME" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Attention à bien exécuter les cellules de code suivantes les unes après les autres. Il est normal que rien ne s'affiche lors de l'exécution de certaines cellules. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Import des bibliothèques utiles" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt # bibliothèque obligatoire pour créer des graphiques\n", "import numpy as np # bibliothèque utile pour déterminer la valeur moyenne, l'écart-type \n", " # et l'incertitude-type de répétabilité" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Création de la liste contenant les valeurs de l'échantillon" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pour créer un histogramme puis réaliser l'étude statistique sous Python, il faut tout d'abord créer une liste contenant les valeurs de l'échantillon. \n", "\n", "On peut aussi créer un tableau numpy grâce à la fonction np.array() de la bibliothèque numpy as np." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "Veprouvette =[49.61,49.55,50.91,50.87,48.03,50.29,48.58,48.06,50.06,50.72,48.95,49.4,49.21,49.31,49.78,48.77] " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Comment créer et paramétrer un histogramme\n", "\n", "On commence par créer une fenêtre graphique aux dimensions souhaitées grâce à la méthode **plt.figure(num, figsize, dpi)** de la bibliothèque **matplotlib.pyplot** as **plt**. Pour plus d'informations, se référer au notebook graphiques_partie_1.\n", "\n", "Puis on crée l'histogramme à l'aide de la méthode **plt.hist(x,bins,range,align,orientation,rwidth,log,color,edgecolor,label)** de la bibliothèque **matplotlib.pyplot** as **plt**\n", "\n", "Voici les principaux paramètres de cette méthode, sachant qu'il n'est pas obligatoire de tous les spécifier. Dans ce cas, ils prendront leur valeur par défaut. \n", "D'autres paramètres existent, pour plus d'informations : \n", "https://matplotlib.org/api/_as_gen/matplotlib.pyplot.hist.html?highlight=hist#matplotlib.pyplot.hist\n", "\n", "- **x** : tableau contenant les valeurs de l'échantillon\n", "- **bins** : le nombre d'intervalles donc de barres ; optionnel, la valeur par défaut est 10.\n", "- **range** : donne les valeurs limites de l'axe des abscisses (xmin,xmax) ; optionnel\n", "- **align** : {'left', 'mid', 'right'}; optionnel, La valeur par défaut est 'mid'\n", "\n", " 'left': la barre est centrée sur le côté gauche de l'intervalle\n", " 'mid': la barre est centrée sur le centre de l'intervalle\n", " 'right': la barre est centrée sur le côté droit de l'intervalle\n", " \n", "- **orientation** : {'horizontal', 'vertical'}; optionnel, la valeur par défaut est 'vertical'\n", "- **rwidth** : largeur des barres sous la forme d'une fraction de l'intervalle ; optionnel, la valeur par défaut est 1.\n", "- **log** : booléen, permet d'afficher une échelle logarithmique pour l'axe des abscisses si log=True ; optionnel, valeur par défaut :False \n", "- **color** : couleur des barres ; optionnel\n", "- **edgecolor** : couleur du contour des barres ; optionnel\n", "- **label** : permet de légender l'histogramme ; optionnel. Attention, son utilisation nécessite l'appel de la méthode **plt.legend()** dans la suite du programme\n", "\n", "On peut ensuite afficher un titre, légender les axes de l'histogramme tout comme on le ferait sur un graphique grâce aux méthodes **plt.title(), plt.xlabel(), plt.ylabel()...** \n", "Enfin, on affiche l'histogramme grâce à la méthode **plt.show()**.\n", "\n", "Pour plus d'informations concernant ces dernières méthodes, se référer au notebook graphiques_partie_1." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Premier exemple : Utilisation de la méthode plt.hist() sans passage de paramètre" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(12,10))\n", "plt.hist(Veprouvette)\n", "plt.title(\"Volume d'eau contenu par une éprouvette graduée pour 50mL mesuré\")\n", "plt.xlabel(\"Volume (mL)\")\n", "plt.ylabel(\"Fréquence\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Deuxième exemple : Utilisation de la méthode plt.hist() avec passage de paramètres" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(12,10))\n", "plt.hist(Veprouvette,bins=20,range=(45,55),align=\"mid\",rwidth=0.9,color=\"y\",edgecolor=\"r\",label=\"éprouvette\")\n", "plt.title(\"Volume d'eau contenu par une éprouvette graduée pour 50mL mesuré\")\n", "plt.xlabel(\"Volume (mL)\")\n", "plt.ylabel(\"Fréquence\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Et si l'on veut afficher plusieurs histogrammes dans la même fenêtre graphique?\n", "\n", "Il suffit d'appeler la méthode **plt.hist()** autant de fois que nécessaire. Les paramètres sont alors très utiles!\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "Vbecher=[50.65,48.26,47.83,47.76,50.26,47.23,43.88,43.92,48.69,48.66,43.67,47.53,49.55,50.64,43.8,48.53]\n", "Veprouvette =[49.61,49.55,50.91,50.87,48.03,50.29,48.58,48.06,50.06,50.72,48.95,49.4,49.21,49.31,49.78,48.77]\n", "Vfiole=[49.74,49.77,49.71,49.75,49.52,49.8,49.61,49.56,49.65,49.65,49.52,49.64,49.74,49.81,49.5,49.59]\n", "plt.figure(figsize=(12,10))\n", "plt.hist(Vbecher,bins=32,range=(43,51),align=\"left\",rwidth=0.3,color=\"r\",label=\"becher\")\n", "plt.hist(Veprouvette,bins=32,range=(43,51),align=\"mid\",rwidth=0.3,color=\"b\",label=\"éprouvette\")\n", "plt.hist(Vfiole,bins=32,range=(43,51),align=\"right\",rwidth=0.3,color=\"g\",label=\"fiole jaugée\")\n", "plt.title(\"Volume d'eau contenu par un bécher, une éprouvette graduée ou une fiole jaugée pour 50mL mesuré\")\n", "plt.xlabel(\"Volume (mL)\")\n", "plt.ylabel(\"Fréquence\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Détermination de la moyenne, de l'écart-type, de l'effectif et de l'incertitude-type de répétabilité (ou incertitude de type A)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On utilise les fonctions de la bibliothèque **numpy** as **np**:\n", "\n", "- la fonction **np.mean(x)** permet de calculer la valeur moyenne de l'échantillon x\n", "- la fonction **np.std(x)** permet de calculer l'écart-type de l'échantillon x\n", "- la fonction **np.sqrt(a)** permet de calculer la racine carrée du nombre a et sera utile lors du calcul de l'incertitude-type de répétabilité.\n", "\n", "La fonction **len(x)** permet de calculer l'effectif (nombre de valeurs) de l'échantillon x.\n", "\n", "Pour ces trois fonctions, x peut être un tableau, un p-uplet (tuple en anglais), un tableau numpy. Pour plus de renseignements sur les listes, tuples ou les tableaux numpy, se référer aux **notebooks Listes** et **Tableaux numpy**.\n", "\n", "L'incertitude-type de répétabilité a pour formule $U(x)=\\frac{écart-type(x)}{\\sqrt{effectif(x)}}$\n", "\n", "Attention, ce programme n'arrondit pas les valeurs et n'exprime pas avec le bon nombre de chiffres significatifs la valeur moyenne et l'incertitude-type. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Le volume moyen : 49.506249999999994 mL\n", "L'écart-type vaut : 0.8814042418209694 mL\n", "Le nombre de mesures vaut : 16\n", "L'incertitude-type de répétabilité de deltat vaut : 0.22035106045524236 mL\n" ] } ], "source": [ "Vmoy=np.mean(Veprouvette)\n", "ecarttype=np.std(Veprouvette)\n", "effectif=len(Veprouvette)\n", "incertitudetype=ecarttype/np.sqrt(effectif)\n", "\n", "print(\"{0:55}\".format(\"Le volume moyen :\"),Vmoy,\"mL\")\n", "print(\"{0:55}\".format(\"L'écart-type vaut :\"),ecarttype,\"mL\")\n", "print(\"{0:55}\".format(\"Le nombre de mesures vaut :\"),effectif)\n", "print(\"{0:55}\".format(\"L'incertitude-type de répétabilité de deltat vaut :\"),incertitudetype,\"mL\")" ] } ], "metadata": { "celltoolbar": "Format de la Cellule Texte Brut", "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": "3.6.9" } }, "nbformat": 4, "nbformat_minor": 4 }