RMS spread versus raw root mean square
= RMS spread versus raw root mean square
{c}
{title2=$x_{\rm rms}^2=\mu^2+\sigma^2$}
The raw <root mean square> of a random variable is $\sqrt{E[X^2]}$, whereas its r.m.s. fluctuation about its <mean> is the <standard deviation> $\sqrt{E[(X-\mu)^2]}$. The former cannot be smaller than $|\mu|$. Experimental phrases such as r.m.s. <noise> or <temperature> spread usually refer to the latter and should state the reference level.