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# When to use the geometric mean?

This is better documented elsewhere, but I could not find a quick reference on the web as to when you’d want to use the geometric mean instead of the arithmetic (usual) mean.

- Suppose that I’m 30% richer than last year, but last year I was 20% richer than the year before… what is the average growth? Well, my current wealth is 1.3
*1.2**w*if*w*is my wealth two years ago. I can expect that if*t*is the average growth factor over the last two years, then my current wealth is*t**t**w*. Setting*t*= 1.25 is the wrong answer. In such a case, choosing*t*= sqrt(1.3 * 1.2) solves the problem. - Another case where the geometric mean makes sense is when you are stuck averaging numbers that are not comparable like the time necessary to build a data cube, versus the average query time. Indeed, if
*a*and*b*are two numbers and*a*is much smaller than*b*, then (2*a*+*b*)/2 is about the same as (*a+b*)/2. One component of your system is significantly worse and yet, you get the same**average**performance? That’s wrong. Computing sqrt (2*ab*) seems to make much more sense.