# 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 ${x}_{1},{x}_{2},.....,{x}_{n}$ is typically denoted by $\overline{x}$, 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 $\overline{x}$) 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 $p\left(x\right)$, and then adding all these products together, giving $\mu =\sum _{}xp\left(x\right)$. 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.

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

**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 Code Editor:**

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**Previous:** Write a NumPy program to compute the weighted of a given array.

**Next:** Write a NumPy program to compute the covariance matrix of two given arrays.

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