Root mean square

In mathematics, the root mean square (abbrev. RMS, RMS or rms) of a set of numbers is the square root of the set's mean square.^[1] Given a set ${\displaystyle x_{i}}$, its RMS is denoted as either ${\displaystyle x_{\mathrm {RMS} }}$ or ${\displaystyle \mathrm {RMS} _{x}}$. The RMS is also known as the quadratic mean (denoted ${\displaystyle M_{2}}$),^[2][3] a special case of the generalized mean. The RMS of a continuous function is denoted ${\displaystyle f_{\mathrm {RMS} }}$ and can be defined in terms of an integral of the square of the function. In estimation theory, the root-mean-square deviation of an estimator measures how far the estimator strays from the data.