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) |

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.

© 1996-9

1999-05-25