Numpy std() - Standard Deviation

Numpy Standard Deviation

Standard Deviation is the measure by which the elements of a set are deviated or dispersed from the mean.

In this tutorial, we will learn how to find the Standard Deviation of a NumPy Array.

In NumPy, you can find the Standard Deviation of a NumPy Array using numpy.std() function.

We shall go through examples covering different scenarios to understand the usage of numpy std() function.

Examples

1. Standard Deviation of 1D Array

In this example, we shall take a Numpy 1D Array with three elements and find the standard deviation of the array.

Python Program

import numpy as np

#initialize array
A = np.array([2, 1, 6])

#compute standard deviation
output = np.std(A)

print(output)

Output

2.160246899469287

Mathematical Proof

Mean = (2 + 1 + 6)/3
     = 3

Standard Deviation = sqrt( ((2-3)^2 + (1-3)^2 + (6-3)^2)/3 )
                   = sqrt( (1+4+9)/3 )
                   = sqrt(14/3)
                   = sqrt(4.666666666666667)
                   = 2.160246899469287

2. Standard Deviation of 2D Array

In this example, we shall take a Numpy 2D Array of size 2x2 and find the standard deviation of the array.

Python Program

import numpy as np

#initialize array
A = np.array([[2, 3], [6, 5]])

#compute standard deviation
output = np.std(A)

print(output)

Output

1.5811388300841898

Mathematical Proof

Mean = (2 + 3 + 6 + 5)/4
     = 4

Standard Deviation = sqrt( ((2-4)^2 + (3-4)^2 + (6-4)^2 + (5-4)^2)/4 )
                   = sqrt( (4+1+4+1)/4 )
                   = sqrt(10/4)
                   = sqrt(2.5)
                   = 1.5811388300841898

3. Standard Deviation of array along an axis

You can also find the standard deviation of a Numpy Array along axis.

In this example, we shall take a Numpy 2D Array of size 2x2 and find the standard deviation of the array along an axis.

Python Program

import numpy as np

#initialize array
A = np.array([[2, 3], [6, 5]])

#compute standard deviation
output = np.std(A, axis=0)

print(output)

Output

[2. 1.]

Mathematical Proof

1st element
======================

mean = (2+6)/2 = 4

standard deviation = sqrt( ( (2-4)^2 + (6-4)^2 )/2 )
                   = sqrt( 4 )
                   = 2.0

2nd element
======================

mean = (3+5)/2 = 4

standard deviation = sqrt( ( (3-4)^2 + (5-4)^2 )/2 )
                   = sqrt( 1 )
                   = 1.0

Summary

In this NumPy Tutorial, we learned how to compute standard deviation of Numpy Array using numpy.std() function, with the help of well detailed examples.