why do we use rms?

[thebillsfan]

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why don't we use the mean of the absolute value? and why is the rms different from the mean of the absolute value? intuition says that the mean of the square roots of the squares should be the same as the mean of the absolute value.

 

[kentavr]

why don't we use the mean of the absolute value? and why is the rms different from the mean of the absolute value? intuition says that the mean of the square roots of the squares should be the same as the mean of the absolute value.

Actually, we can use mean of abs. That will be another measure of spread. (it is used in non-parametric statistics theories) However, these two things are not equal. (Your intuition is wrong). RMS more sensitive to outliers(points far from mean) then simple average. The reason to choose RMS vs Average of Abs is that it is easy to work with mathematicaly. Abs does not have first derivative and is not easy to manipulate in calculus.

 

[thebillsfan]

oh i get it, because outliers squared would be HUGE outliers. so its close enough to the simple average that it doesnt make a difference for most purposes?

 

[kentavr]

oh i get it, because outliers squared would be HUGE outliers. so its close enough to the simple average that it doesnt make a difference for most purposes?

Yes, they represent the same thing in general. That is just a human convention to measure the statistical deviations somehow. No physical phenomena stays behind that. Just comfort to calculate and some useful properties.