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3 Ways To Compute A Weighted Average in Python

In this brief tutorial, I show how to compute weighted averages in Python either defining your own functions or using NumPy

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• Programming For Data Science In Python (Nano-Degree)
• Practicing Statistics Interview Questions In Python

Hope you’ll find them useful too! Now enjoy the article :D

When To Use A Weighted Average?

Suppose you had to analyze the table below, showing the yearly salary for the employees of a small company divided in five groups (from lower to higher salary):

If you computed the simple average of the Salary Per Year column you would obtain:

But is £62,000 an accurate representation of the average salary across the groups? Because data comes already aggregated and each group has a different Employees Number, the average Salary Per Year for each group weights differently in the overall average. In computing the simple average, the same weight was assigned to each group leading to a biased result.

In this cases, the solution is to take into account the weight of each group by computing a weighted average that can be represented algebraically with the formula:

Where x represents the distribution ( Salary Per Year ) and w represents the weight to be assigned ( Employees Number). Given that the table includes five groups, the formula above becomes:

An by replacing x and w with actual figures, you should obtain the result below:

Note how taking weights into account, the average Salary Per Year across the groups is almost £18,000 lower than the one computed with the simple average and this is an accurate way to describe our dataset given the number of employees in each group.

Now that the theory has been covered, let’s see how to obtain a weighted average in Python using 3 different methods. In order to do that, the first step is to import packages and the employees_salary table itself:

import pandas as pd
from numpy import average

df = pd.read_csv(‘C:/Users/anbento/Desktop/employee_salary.csv’)

df.head()
distribution = df[‘salary_p_year’]
weights = df[‘employees_number’]

Method #1 : Function Using List Comprehension

If you wish to code your own algorithm, the first very straightforward way to compute a weighted average is to use list comprehension to obtain the product of each Salary Per Year with the corresponding Employee Number ( numerator ) and then divide it by the sum of the weights ( denominator).

Output:
44225.35

The function above could easily be rewritten as a one liner:

Output:
44225.35

Method #2: Function Using Zip()

Instead of using list comprehensions, you could simply start from and empty list ( weighted_sum ) and append the product of the average salary for each group by its weight . The zip() function is very handy as it generates an iterator of tuples that helps pairing each salary to the corresponding weight .

Output:
44225.35

Method #3: Using Numpy Average() Function

The numpy package includes an average() function (that has been imported above) where you can specify a list of weights to calculate a weighted average. This is by far the easiest and more flexible method to perform these kind of computations in production:

Output:
44225.35

Conclusion

In this brief tutorial, we learnt how weighted averages should be the preferred option every time data is presented in an aggregated or grouped way, where some quantities or frequencies can be identified. We also found at least 3 methods to compute a weighted average with Python either with a self-defined function or a built-in one. I would be curious to know if you use any other algorithm or package to compute weighted averages, so please do leave a comment!

A Note For My Readers

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