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 ,
denotes the mean of the values .
variate from a continuous distribution ,
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
The root-mean-square is the special case
of the power mean.
Hoehn and Niven (1985) show that
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.
See also Arithmetic-Geometric Mean
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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 Princeton, NJ: Van Nostrand, pp. 59-60,
of Statistics, Pt. 1, 3rd ed. Referenced on Wolfram|Alpha Root-Mean-Square
Cite this as:
Weisstein, Eric W. "Root-Mean-Square."
From --A Wolfram Web Resource. MathWorld https://mathworld.wolfram.com/Root-Mean-Square.html