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

Last update on May 28 2022 13:28:55 (UTC/GMT +8 hours)

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 $x_{1}, x_{2}, . . . . ., x_{n}$ is typically denoted by $\bar{x}$ , 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 $\bar{x}$ ) 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 $p (x)$ , and then adding all these products together, giving $μ = \sum_{} x p (x)$ . 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:")
print(x)
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-Numpy Code Editor:

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Find current directory and file's directory:

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Documentation references for the modules, constants and functions used above:

The os and os.path modules.

The __file__ constant

os.path.realpath(path) (returns "the canonical path of the specified filename, eliminating any symbolic links encountered in the path")

os.path.dirname(path) (returns "the directory name of pathname path")

os.getcwd() (returns "a string representing the current working directory")

os.chdir(path) ("change the current working directory to path")

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