NumPy: Compute the weighted average along the specified axis of a given flattened array

NumPy Statistics: Exercise-12 with Solution

Write a Python NumPy program to compute the weighted average along the specified axis of a given flattened array.

The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. The notion of weighted mean plays a role in descriptive statistics and also occurs in a more general form in several other areas of mathematics.

Basic example
Given two school classes, one with 20 students, and one with 30 students, the grades in each class on a test were:
Morning class = 62, 67, 71, 74, 76, 77, 78, 79, 79, 80, 80, 81, 81, 82, 83, 84, 86, 89, 93, 98
Afternoon class = 81, 82, 83, 84, 85, 86, 87, 87, 88, 88, 89, 89, 89, 90, 90, 90, 90, 91, 91, 91, 92, 92, 93, 93, 94, 95, 96, 97, 98, 99
The straight average for the morning class is 80 and the straight average of the afternoon class is 90. The straight average of 80 and 90 is 85, the mean of the two class means. However, this does not account for the difference in number of students in each class (20 versus 30); hence the value of 85 does not reflect the average student grade (independent of class). The average student grade can be obtained by averaging all the grades, without regard to classes (add all the grades up and divide by the total number of students):
$\overline{x} = \frac{4300}{50} = 86.$
Or, this can be accomplished by weighting the class means by the number of students in each class (using a weighted mean of the class means):
$\overline{x} = \frac{\left(20 x 80\right)+\left(30 x 90\right)}{20 + 30} = 86.$
Thus, the weighted mean makes it possible to find the average student grade in the case where only the class means and the number of students in each class are available.

Sample Solution:

Python Code:

# Importing the NumPy library
import numpy as np

# Creating a 3x3 array and reshaping it
a = np.arange(9).reshape((3,3))

# Displaying the original flattened array
print("Original flattened array:")
print(a)

# Calculating the weighted average along the specified axis (axis=1) of the above flattened array using specified weights
print("Weighted average along the specified axis of the above flattened array:")
print(np.average(a, axis=1, weights=[1./4, 2./4, 2./4])) 

Sample Output:

Original flattened array:
[[0 1 2]
 [3 4 5]
 [6 7 8]]
Weighted average along the specified axis of the above flattened array:
[1.2 4.2 7.2]

Explanation:

In the above exercise –

a = np.arange(9).reshape((3,3)): A 3x3 array is created where each element of the array is a number between 0 and 8.

np.average(a, axis=1, weights=[1./4, 2./4, 2./4]): This line of code calculates the weighted average of the elements in each row of the array a using the specified weights [1./4, 2./4, 2./4].

In the above code axis=1 specifies that the operation is to be performed on the rows of the array and weights=[1./4, 2./4, 2./4] specifies the weights to be used for the calculation.

Python-Numpy Code Editor:

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