How to average hues

Recently I needed some software to be able to average the hues in some HSL colors to find the hue between them. My first attempt was simple: just treat the hues as a number from 0° to 360° and average them. That approach did not work as I expected. The solution was to take a circular mean; this post will explain that. Here’s what a naive arithmetic mean would look like for averaging 40° and 300°. The average of two numbers is always equidistant between those two numbers, so the average sits righ...