Root mean square

In mathematics, the root mean square (abbrev. RMS, rms or rms) of a set of values is the square root of the set's mean square. Given a set x i {\displaystyle x_{i}} , its RMS is denoted as either x R M S {\displaystyle x_{\mathrm {RMS} }} or R M S x {\displaystyle \mathrm {RMS} _{x}} . The RMS is also known as the quadratic mean (denoted M 2 {\displaystyle M_{2}} ), a special case of the generalized mean. The RMS of a continuous function is denoted f R M S {\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.