Python numpy average of an Array

The Python numpy average() function helps compute the weighted average of a given array along the specified axis.

Python numpy average Syntax

The syntax of this statistical method is

numpy.average(a, axis = None, weights = None, returned = False, *, keepdims = <no value>)

The arguments are

a = Array
If you specify the axis value, this function will only calculate the average for that axis.
weights – It will calculate the weighted average if you define the weights.
returned – if you set this to true, it will return the sum of weights.
keepdims – To retain the original shape.

Difference between average() and mean()

Both the average() and mean() functions will calculate the average of the ndarray. However, Python numpy average() has a weight argument to compute the weighted average.

Python numpy average Example

In this example, we declared a one-dimensional ndarray of five integers. Next, we calculate both the normal and weighted average of the array.

import numpy as np

a = np.array([10, 20, 30, 40, 50])

b  = np.average(a)
print(b)

c = np.average(a, weights = [2, 4, 6, 8, 10])
print(c)

d = np.average(a, weights = [2, 4, 6, 8, 10], returned = True)
print(d)

30.0
36.666666666666664
(36.666666666666664, 30.0)

(10 * 2 + 20* 4 + 30 * 6 + 40* 8 + 50* 10) / (2 + 4 + 6+ 8 + 10)

= (20 + 80 + 180 + 320 + 500) / 30

= 1100 / 30

= 36.666666666666664

In the last line, we used returned = True will return the sum of the given weights. And the sum = 2 + 4 + 6+ 8 + 10 = 30

Two-Dimensional example

In this program, we will declare a two-dimensional square matrix.

import numpy as np

a = np.array([[10, 20], [30, 40]])

b  = np.average(a)
print(b)

c = np.average(a, weights = [[3, 5], [6, 2]])
print(c)

25.0
24.375

b = (10 + 20 + 30 + 40) \ 4 = 100 / 4 = 25

c = (10 * 3 + 20* 5 + 30 * 6 + 40* 2) / (3 + 5 + 6 + 2) = 390/ 16

c = 24.375

By default, this Python function calculates the average for the whole numpy array. However, we can compute the row and column-wise by specifying the axis value. For instance, in the below example, axis = 0 calculates the average for each column, and axis = 1 calculates each row.

The result will reshape if you use the keepdims argument and assigned True value.

import numpy as np

a = np.arange(20).reshape(4, 5)
print(a)

b  = np.average(a)
print(b)

c = np.average(a, axis = 0)
print(c)

d = np.average(a, axis = 1)
print(d)

e = np.average(a, axis = 1,  keepdims = True)
print(e)

[[ 0  1  2  3  4]
 [ 5  6  7  8  9]
 [10 11 12 13 14]
 [15 16 17 18 19]]

9.5

[ 7.5  8.5  9.5 10.5 11.5]

[ 2.  7. 12. 17.]

[[ 2.]
 [ 7.]
 [12.]
 [17.]]

In this example, we used arange and reshape methods to generate a 2D array of 4 * 3 size and the numbers from 0 to 11. Next, we used axis and weights so that Python would calculate the weighted average of numpy array rows and columns.

import numpy as np

a = np.arange(12).reshape(4, 3)
print(a)

b  = np.average(a)
print(b)

c = np.average(a, axis = 0, weights = [3, 5, 7, 9])
print(c)

d = np.average(a, axis = 1, weights = [2, 4, 6])
print(d)

[[ 0  1  2]
 [ 3  4  5]
 [ 6  7  8]
 [ 9 10 11]]

5.5

[5.75 6.75 7.75]

[ 1.33333333  4.33333333  7.33333333 10.33333333]

For b = (0 + 1 + 2+ 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11) / 12 = 66/12 = 5.5

First Column in c = (0 * 3 + 3 * 5 + 6 * 7 + 9 * 9) / (3 + 5 + 7 + 9) = 138 / 24 = 5.75

First Row in d = (0 * 2 + 1 * 4 + 2 * 6) / (2 + 4 + 6) = 16 / 12 = 1.33333333