Calculating the Running Mean of a Sequence in Python

Learn how to calculate the running mean of a sequence in Python easily with our step-by-step guide and example!
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Understanding the Running Mean

Have you ever found yourself needing to calculate the average of a sequence of numbers, but with a twist? That's where the running mean comes in! The running mean, or cumulative average, is a sequence of averages calculated on the fly. Each element in the output array represents the average of all the previous elements in the input array up to that index.

So, if your input is [1, 2, 3], the running mean outputs [1, 1.5, 2]. Here’s the breakdown:

The average of the first element (1) is simply 1.

The average of the first two elements (1, 2) is (1 + 2) / 2 = 1.5.

The average of the first three elements (1, 2, 3) is (1 + 2 + 3) / 3 = 2.

This guide will guide you through how to compute the running mean in Python, step by step, so you can easily incorporate this into your projects.

How to Calculate the Running Mean

To create your function for calculating the running mean, follow these steps:

Step 1: Create Partial Arrays

The first thing you need to do is create partial arrays from the initial segment of the sequence leading up to the current index. For the input [1, 2, 3], the partial arrays are:

At index 0: [1]

At index 1: [1, 2]

At index 2: [1, 2, 3]

This allows you to focus on each subset of the sequence and calculate the average.

Step 2: Calculate the Average of Each Partial Array

Once you have your partial arrays, the next step is to calculate the average for each of them using the formula:

[[See Video to Reveal this Text or Code Snippet]]

Putting this all together in a Python function gives the following code:

[[See Video to Reveal this Text or Code Snippet]]

Explanation of the Code

Function Definition: We define a function running_mean that takes a sequence as an argument.

List Comprehension: We use list comprehension to iterate over the range of indices of the sequence. The enumeration is the sum of elements up to the i-th index divided by (i+ 1) to account for zero-based index.

Output: The resulting list contains all the averages of the initial portions of the input array.

Conclusion

Calculating the running mean can be a valuable tool in data analysis and statistical applications. By following this guide, you can efficiently compute the running mean in Python. With just a simple function, you can transform your list of numbers into a meaningful sequence of averages!

So, the next time you need running means, remember this straightforward approach to achieve it effortlessly.