Statistiques Descriptives à 1 variable (Python)

Introduction

Cet article introduit, comment avec le langage python, obtenir
différents éléments relatifs aux statistiques descriptives à 1 variable ( moyenne, médiane, etc et les représentations graphiques usuelles). Pour illustrer l'article on a utilisé un exemple provenant d'un cours video sur une introduction aux statistiques descriptives
(voir les statistiques descriptives ).

• Télécharger le fichier de données: [attachment:203]
• Télécharger le code python: [attachment:204]
• Exécution du code: python DescriptiveStatistics_01.py

Description intrinsèque

La Moyenne

np.mean(Taille)

La Médiane

np.median(Taille)

Le mode

stats.mode(Taille,axis=0)

Le maximum minimum

max(Taille), min(Taille)

L'écart type (et la variance)

np.std(Taille)
np.std(Taille, ddof=1)

Les quartiles

print 'First quartile: ', stats.scoreatpercentile(Taille, 25)
print 'Second quartile: ', stats.scoreatpercentile(Taille, 50)
print 'Third quartile: ', stats.scoreatpercentile(Taille, 75)

Exemple

• Moyenne (mean): 169.7
• L'écart type (standard deviation) 9.95540054443
• L'écart type non biasé (standard deviation unbiased): 10.2140254449
• La médiane (median): 167.5
• Maximum et minimum (Max and Min Value): 190.0, 150.0
• Étendue (Range): 40.0
• Mode (Mode): (array([ 164.]), array([ 3.]))
• First quartile: 163.75
• Second quartile: 167.5
• Third quartile: 175.5

Représentations graphiques

Histogramme

(Histogram)

fig = plt.figure()
plt.xticks(x_pos, people,rotation=45)
plt.ylabel(r'Absolute Frequency $n_i$')
bar1 = plt.bar(X,AbsoluteFrequency,width=1.0,bottom=0,color='Green',alpha=0.65,label='Legend')
plt.savefig('Histogram.png', bbox_inches='tight')
plt.show()

Fonction de répartition

(Cumulative distribution function)

fig = plt.figure()
for i in np.arange(NbClass):
    plt.plot([CumulativeFrequency_xStart[i],CumulativeFrequency_xEnd[i]], \
    [CumulativeFrequency[i],CumulativeFrequency[i]], 'k--')
    if i < NbClass - 1:
        plt.scatter(CumulativeFrequency_xEnd[i], CumulativeFrequency[i], \
        s=80, facecolors='none', edgecolors='r')
    if i == 0:
        plt.plot([CumulativeFrequency_xStart[i],CumulativeFrequency_xEnd[i]], \
        [0,CumulativeFrequency[i]], 'r--')
    else:
        plt.plot([CumulativeFrequency_xStart[i],CumulativeFrequency_xEnd[i]], \
        [CumulativeFrequency[i-1],CumulativeFrequency[i]], 'r--')    
plt.xlim(0,NbClass)
plt.ylim(0,1)
plt.xticks(x_pos, LabelList,rotation=45)
plt.title("Cumulative Distribution Function")
plt.savefig('CumulativeDistributionFunction.png', bbox_inches='tight')
plt.show()

Boîte à moustaches

(Box Plot)

fig = plt.figure()
plt.xticks([0], ['Taille'])
plt.boxplot(Taille)
plt.savefig('BoxPlot.png', bbox_inches='tight')
plt.show()

Code Python

Code Source:

from scipy import stats

import numpy as np
import matplotlib.pyplot as plt
import math

# '---------- Read Data ----------'

Taille, Poids = np.loadtxt("data.txt", unpack=True, skiprows=1)

Taille = np.sort(Taille)

# '---------- Print Descriptive statistics: Continuous Case ----------'

print Taille
print 'Taille Dim: ', Taille.shape
print 'mean', np.mean(Taille)
print 'std', np.std(Taille)
print 'std (unbiased): ', np.std(Taille, ddof=1)
print 'Median: ', np.median(Taille)
print 'Max and Min Value: ', max(Taille), min(Taille)
print 'Range: ', max(Taille) - min(Taille)
print 'Mode: ', stats.mode(Taille,axis=0)
print 'First quartile: ', stats.scoreatpercentile(Taille, 25)
print 'Second quartile: ', stats.scoreatpercentile(Taille, 50)
print 'Third quartile: ', stats.scoreatpercentile(Taille, 75)

# '---------- Discrete Case ----------'

NbData = Taille.shape[0]
NbClass = 4 #int( math.log(NbData,2) ) + 1
Range = max(Taille) - min(Taille)
ClassRange = float( Range ) / NbClass

print 'NbData: ', NbData
print 'NbClass: ', NbClass
print 'ClassRange: ', ClassRange

X = np.arange(NbClass)
AbsoluteFrequency = np.zeros(NbClass)
for i in np.arange(NbData-1):
    c = int((Taille[i]-min(Taille))/ClassRange) 
    AbsoluteFrequency[c] = AbsoluteFrequency[c] + 1
AbsoluteFrequency[NbClass-1] = AbsoluteFrequency[NbClass-1] + 1

ClassLabel = []
j = round(min(Taille),2)
for i in np.arange(NbClass+1):
    ClassLabel.append(j)
    j = round(j + ClassRange,2)
LabelList = (ClassLabel)
x_pos = np.arange(len(LabelList))

# '---------- Plot Absolute Frequency Histogram ----------'

fig = plt.figure()
plt.xticks(x_pos, LabelList,rotation=45)
plt.ylabel(r'Absolute Frequency $n_i$')
bar1 = plt.bar(X,AbsoluteFrequency,\
       width=1.0,bottom=0,color='Green',alpha=0.65,label='Legend')
plt.savefig('Histogram.png', bbox_inches='tight')
plt.show()

RelativeFrequency = np.zeros(NbClass)
RelativeFrequency = AbsoluteFrequency / NbData

# '---------- Plot Cumulative distribution function ----------'

CumulativeFrequency = np.zeros(NbClass)
CumulativeFrequency_xStart = np.zeros(NbClass)
CumulativeFrequency_xEnd = np.zeros(NbClass)
j = 0 
k = 0
for i in np.arange(NbClass):
    CumulativeFrequency[i] = j + RelativeFrequency[i]
    j = j + RelativeFrequency[i]
    CumulativeFrequency_xStart[i] = k
    CumulativeFrequency_xEnd[i] = k + 1
    k += 1

fig = plt.figure()
for i in np.arange(NbClass):
    plt.plot([CumulativeFrequency_xStart[i],CumulativeFrequency_xEnd[i]], \
    [CumulativeFrequency[i],CumulativeFrequency[i]], 'k--')
    if i < NbClass - 1:
        plt.scatter(CumulativeFrequency_xEnd[i], CumulativeFrequency[i], \
        s=80, facecolors='none', edgecolors='r')
    if i == 0:
        plt.plot([CumulativeFrequency_xStart[i],CumulativeFrequency_xEnd[i]], \
        [0,CumulativeFrequency[i]], 'r--')
    else:
        plt.plot([CumulativeFrequency_xStart[i],CumulativeFrequency_xEnd[i]], \
        [CumulativeFrequency[i-1],CumulativeFrequency[i]], 'r--')    
plt.xlim(0,NbClass)
plt.ylim(0,1)
plt.xticks(x_pos, LabelList,rotation=45)
plt.title("Cumulative Distribution Function")
plt.savefig('CumulativeDistributionFunction.png', bbox_inches='tight')
plt.show()

# '---------- Plot Box Plot ----------'

fig = plt.figure()
plt.xticks([0], ['Taille'])
plt.boxplot(Taille)
plt.savefig('BoxPlot.png', bbox_inches='tight')
plt.show()

Références

Liste non exhaustive des pages web consultées lors de la rédaction de cet article: