Root-Mean-Square

For a set of numbers or values of a discrete distribution , ..., , the root-mean-square (abbreviated "RMS" and sometimes called the quadratic mean), is the square root of mean of the values , namely

			(1)
			(2)
			(3)

where denotes the mean of the values .

For a variate from a continuous distribution ,

(4)

where the integrals are taken over the domain of the distribution. Similarly, for a function periodic over the interval ], the root-mean-square is defined as

(5)

The root-mean-square is the special case of the power mean.

Hoehn and Niven (1985) show that

(6)

for any positive constant .

Physical scientists often use the term root-mean-square as a synonym for standard deviation when they refer to the square root of the mean squared deviation of a signal from a given baseline or fit.

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