RMS spread versus raw root mean square ($x_{\mathrm{rms}}^2={\mu }^2+{\sigma }^2$)

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.