Contraharmonic mean

So, if you have a bunch of numbers and you want to find the “average” of them, you add them up and divide by how many there are. That’s called the arithmetic mean.

But sometimes, you want to find a different kind of average. One kind is called the harmonic mean, and it’s like if you want to find the “average” of how fast you were driving over a distance. This is because the harmonic mean gives more weight to smaller numbers, which is like how your overall speed would be affected more by not driving fast enough for a little bit, than by driving really fast for a little bit.

But what if you want to find an average of how much you liked or disliked different things? The contraharmonic mean can help you out there. This kind of average gives more weight to larger numbers, because just like how driving really fast for a little bit doesn’t affect your overall speed as much, really liking or disliking one thing doesn’t affect your overall feelings as much.

So, if you wanted to find the contraharmonic mean of numbers like 5, 7, and 10, you would do this:

First, you would add up the squares of each number, so 5^2 + 7^2 + 10^2 = 194.

Then you would add up the numbers themselves, so 5 + 7 + 10 = 22.

Then you would divide the first number by the second number, so 194/22 = 8.81818181...

And that’s your contraharmonic mean!