standard deviation help

[BruceZ]

Here's an everyday example of rms average. In the US we say the AC coming from your wall is 120 volts. This is a sine wave, but if we measured the amplitude we would see it actually goes up to a peak of 170 volts. The 120 volts is an rms average. It is the result of integrating [170*sin(x)]^2 over a period of 2*pi, dividing by 2*pi, and taking the square root. This is the square root of the average of the squares of all the amplitudes which turns out to be 170/sqrt(2) = 120 rms. It will produce the same power as a constant DC voltage of 120 volts. It is not the same as the average excursion from 0 ignoring sign, which turns out to be 170*2/pi = 108 volts.