## 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) (2)

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.

See also Arithmetic-Geometric Mean, Arithmetic-Harmonic Mean, Generalized Mean, Geometric Mean, Harmonic Mean, Harmonic-Geometric Mean, Mean, Median (Statistics), Standard Deviation, Variance

References

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

© 1996-9 Eric W. Weisstein
1999-05-25