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. Please refer to the Python NumPy array article from the Python tutorial page.
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. Also, refer to the Python NumPy sum.
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
24.375b = (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