NumPy: Compute the mean, standard deviation, and variance of a given array along the second axis

NumPy Statistics: Exercise-7 with Solution

Write a NumPy program to compute the mean, standard deviation, and variance of a given array along the second axis.

From Wikipedia: There are several kinds of means in various branches of mathematics (especially statistics).
For a data set, the arithmetic mean, also called the mathematical expectation or average, is the central value of a discrete set of numbers: specifically, the sum of the values divided by the number of values. The arithmetic mean of a set of numbers x1, x2, ....., xn is typically denoted by x¯, pronounced "x bar". If the data set were based on a series of observations obtained by sampling from a statistical population, the arithmetic mean is the sample mean (denoted x¯) to distinguish it from the mean of the underlying distribution.
In probability and statistics, the population mean, or expected value, are a measure of the central tendency either of a probability distribution or of the random variable characterized by that distribution. In the case of a discrete probability distribution of a random variable X, the mean is equal to the sum over every possible value weighted by the probability of that value; that is, it is computed by taking the product of each possible value x of X and its probability px, and then adding all these products together, giving μ = xpx. An analogous formula applies to the case of a continuous probability distribution. Not every probability distribution has a defined mean; see the Cauchy distribution for an example. Moreover, for some distributions the mean is infinite.

Sample Solution:-

Python Code:

import numpy as np
x = np.arange(6)
print("\nOriginal array:")
r1 = np.mean(x)
r2 = np.average(x)
assert np.allclose(r1, r2)
print("\nMean: ", r1)
r1 = np.std(x)
r2 = np.sqrt(np.mean((x - np.mean(x)) ** 2 ))
assert np.allclose(r1, r2)
print("\nstd: ", 1)
r1= np.var(x)
r2 = np.mean((x - np.mean(x)) ** 2 )
assert np.allclose(r1, r2)
print("\nvariance: ", r1)

Sample Output:

Original array:
[0 1 2 3 4 5]

Mean:  2.5

std:  1

variance:  2.9166666666666665

Python Code Editor:

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