root mean square

Statistic; square root of the mean of the squares

Also known as RMS · quadratic mean · root-mean-square value · RMS value · rms

Instance of: type of statistic
Subclass of: mean
, generalized mean
, quasi-arithmetic mean

Overview

From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0

In mathematics, the root mean square of a set of values is the square root of the set's mean square. Given a set , its RMS is denoted as either or . The RMS is also known as the quadratic mean, a special case of the generalized mean. The RMS of a continuous function is denoted 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.

Overview

All data

18 statements · 11% with external sources · numbers in brackets are citations

Defining formula: x_{\mathrm{q}} = \sqrt{\frac{1}{n} \sum_{i = 1}^n x_n^2}
Different from: root-mean-square value
standard deviation
root-mean-square deviation
In defining formula: x_{\mathrm{q}} symbol represents: root mean square
Less than: cubic mean

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9 identifiers linking root mean square across the web's reference databases

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statements

11%

externally sourced

Source last edited September 8, 2026. AIDb refreshes this page daily.

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AIDb. (2026). root mean square (Q223323). Retrieved from https://aidb.si/e/root-mean-square-Q223323