Statistics

Understanding The Harmonic Mean

Gain an intuitive understanding of the harmonic mean and why it is used.

Image generated by Jacob Ferus using Midjourney.

The harmonic mean has a simple and short mathematical expression, yet it can be hard to understand intuitively. In this article, I will explain it thoroughly, the intuition behind it and when and why it is used.

Understanding Why

Let’s start with two related questions:

A

It takes you two hours to drive from position A to B. The first hour you travel at 100 km/h and the second hour at 80 km/h. What is the average velocity during the trip?

B

You are driving from position A to B which is 10 km. The first 5 km of the trip you travel at 100 km/h and the second 5 km at 80 km/h. What is the average velocity during the trip?

The difference between these questions is what is given when you travel at the different velocities and what is not.

• In A, the total time of travel (2 hours) is known but…