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( Root mean square) In mathematics, the root mean square (abbreviated RMS or rms), also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids.

It can be calculated for a series of discrete values or for a continuously varying function. The name comes from the fact that it is the square root of the mean of the squares of the values. It is a special case of the power mean with the exponent p&_160;=&_160;2.

The RMS of a collection of n values \{x_1,x_2,\dots,x_n\} is

The corresponding formula for a continuous function f(t) defined over the interval T_1 \le t \le T_2 is

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