Root-Mean-Square -- from Wolfram MathWorld

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Root-Mean-Square

The root-mean-square (RMS) of a variate , sometimes called the quadratic mean, is the square root of the mean squared value of :

			(1)
		${sqrt((sum_(i=1)^(n)x_i^2)/n) for a discrete distribution; sqrt((intP(x)x^2dx)/(intP(x)dx)) for a continuous distribution.$	(2)

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

Hoehn and Niven (1985) show that

(3)

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.

REFERENCES:

Hoehn, L. and Niven, I. "Averages on the Move." Math. Mag. 58, 151-156, 1985.

Kenney, J. F. and Keeping, E. S. "Root Mean Square." §4.15 in Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, pp. 59-60, 1962.

CITE THIS AS:

Weisstein, Eric W. "Root-Mean-Square." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Root-Mean-Square.html