# Something I have always wondered

1. Aug 7, 2009

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

2. Aug 10, 2009

### Tac-Tics

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.