Name: Saurabh Dinesh Chaudhari || Div: TEA || Roll No: TEA27
Compute Estimators of the main statistical measures like Mean, Variance, Standard Deviation, Covariance, Correlation and Standard error with respect to any example. Display graphically the distribution of samples.
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
np.random.seed(5)
x = np.random.randint(10,70,10)
y = np.random.randint(20,40,10)
x.sort()
y.sort()
from array import array
array=([18, 19, 24, 26, 45, 46, 48, 49, 57, 64])
array=([27, 27, 32, 32, 33, 35, 36, 36, 36, 37])
def calc_mean(dataset):
'''
Def : Mean is defined as the arithmetic average of
a population.
Formula : (sum of obesrvations)∕(No. of observations)
'''
return dataset.sum()/len(dataset)
def calc_variance(dataset,mean):
'''
Def : Variance is the degree of variation∕spread
in the dataset.
Formula : 1) Σ((X - X_mean)^2) ∕ n
'''
squared_diff = np.square(dataset-mean)
return calc_mean(squared_diff)
def calc_SD(variance):
'''
Def : 1) Standard deviation is the amount of deviation
of points around the mean.
2) Variation but in terms of the actual dataset.
Formula : √(variance)
'''
return np.sqrt(variance)
def calc_covariance(dataset1,dataset2):
'''
Def : Covariance measures the relationship trend
between two sets of data.
Formula : 1) Σ((X - X_mean)*(Y - Y_mean)) ∕ n
'''
mean1 = calc_mean(dataset1)
mean2 = calc_mean(dataset2)
return np.sum(np.multiply(dataset1-mean1,dataset2-mean2))/len(dataset1)
def calc_correlation(dataset1,dataset2):
'''
Def : Covariance measures the relationship trend
between two sets of data.
Formula : 1) Σ((X - X_mean)*(Y - Y_mean)) ∕ √(Σ(X - X_mean)^2*Σ(Y - Y_mean)^2)
'''
mean1 = calc_mean(dataset1)
mean2 = calc_mean(dataset2)
num = np.sum(np.multiply(dataset1-mean1,dataset2-mean2))
de = np.multiply(np.sum(np.square(dataset1-mean1)),np.sum(np.square(dataset2-mean2)))
return num/np.sqrt(de)
def calc_SE(dataset,sd):
'''
Def : The standard error is a statistical term that
easures the accuracy with which a sample
distribution represents a population by using
standard deviation.
Formula : Standard_deviation ∕ √(n)
'''
return sd/np.sqrt(len(dataset))
mean = calc_mean(x)
mean2 = calc_mean(y)
variance = calc_variance(x,mean)
S_D = calc_SD(variance)
covariance = calc_covariance(x,y)
correlation = calc_correlation(x,y)
S_E = calc_SE(x,S_D)
print(mean,mean2,variance,S_D,covariance,correlation,S_E)
39.6 33.1 244.64000000000001 15.640971836813723 49.84 0.9164339069491503 4.946109582287882
Dataset
plt.plot(x,"mo:",label="dataset 1")
plt.plot(y,"go:",label = "dataset 2")
plt.legend(loc="upper left")
Mean
plt.plot(x,"mo:",label="Dataset 1")
plt.axhline(mean,color='b',marker= 'o', linestyle=':',label="Mean")
plt.legend(loc="upper left")
plt.plot(y,"ro:",label="Dataset 2")
plt.axhline(mean2,color='g',marker= 'o', linestyle=':',label="Mean")
plt.legend(loc="upper left")
Correlation
corr = np.correlate(x, y, "same")
plt.plot(list(corr),"go:",label = "Correlation")
Variance
plt.plot(x,"mo:",label="Dataset 1")
plt.axhline(mean,color='g',marker= 'o', linestyle=':',label="Mean")
plt.axhline(variance,color='b',marker= 'o', linestyle=':',label="Variance")
plt.legend(loc="upper left")
Covariance
plt.plot(y,"ro:",label="Dataset 2")
plt.plot(x,"go:",label="Daraset 1")
plt.axhline(covariance,color='b',marker= 'o', linestyle=':',label="covariance")