Spherical mean (statistics)

Okay, buddy. Imagine you're holding a globe. Now, what if we wanted to know something about the temperature or weather all over the globe? How would we figure it out?

Well, one way is to take the average of the temperature or weather data at every single point on the globe. But, that would take a lot of time and work, and we might not even have temperature data for every point!

So instead, we can use something called a spherical mean. This is kind of like finding the average temperature or weather for the whole globe, but we do it in a simpler way.

First, we pick a point on the globe. Let's say it's the North Pole. Then, we draw circles on the globe that are all the same distance away from the North Pole. These circles are called "spheres" because they're round like a ball.

Next, we find the temperature or weather data for every point on each of these spheres, and we take the average of all those data points. This average is called the spherical mean!

We can do this for any point on the globe, not just the North Pole. And, we can use a spherical mean to tell us something about the temperature or weather all over the globe, without having to look at every single point. Cool, huh?