Something I have always wondered

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What is the qualitative difference between rms and the mean of the absolute value? For what datasets do they differ most?
 

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0xDEADBEEF said:
What is the qualitative difference between rms and the mean of the absolute value? For what datasets do they differ most?

Say you take a sample of n test results. Each test result ranges between 0% and 100%. You can then imagine the space of the possible test results as a subset of R^n. The particular sample you drew is then a single point in R^n.

The RMS is proportional to the distance between this point and the origin.

You can see in the formula for RMS, if you move the 1/n term outside of the square root radical, you get pythagoras's theorem.

As far as I know (which isn't much), the mean of the absolute value has no such neat geometric interpretation.
 

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