Root mean square

In mathematics, the root mean square (abbrev. RMS, RMS or rms) of a set of numbers is the square root of the set's mean square.^[1] Given a set $x_{i}$ , its RMS is denoted as either $x_{\mathrm {RMS} }$ or $\mathrm {RMS} _{x}$ . The RMS is also known as the quadratic mean (denoted $M_{2}$ ),^[2]^[3] a special case of the generalized mean. The RMS of a continuous function is denoted $f_{\mathrm {RMS} }$ and can be defined in terms of an integral of the square of the function. In estimation theory, the root-mean-square deviation of an estimator measures how far the estimator strays from the data.

^ "Root-mean-square value". A Dictionary of Physics (6 ed.). Oxford University Press. 2009. ISBN 9780199233991.
^ Thompson, Sylvanus P. (1965). Calculus Made Easy. Macmillan International Higher Education. p. 185. ISBN 9781349004874. Retrieved 5 July 2020.^{[permanent dead link‍]}
^ Jones, Alan R. (2018). Probability, Statistics and Other Frightening Stuff. Routledge. p. 48. ISBN 9781351661386. Retrieved 5 July 2020.

[dicphys-1] "Root-mean-square value". A Dictionary of Physics (6 ed.). Oxford University Press. 2009. ISBN 9780199233991.

[2] Thompson, Sylvanus P. (1965). Calculus Made Easy. Macmillan International Higher Education. p. 185. ISBN 9781349004874. Retrieved 5 July 2020.^{[permanent dead link‍]}

[3] Jones, Alan R. (2018). Probability, Statistics and Other Frightening Stuff. Routledge. p. 48. ISBN 9781351661386. Retrieved 5 July 2020.

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