Mean square explained

In mathematics and its applications, the mean square is normally defined as the arithmetic mean of the squares of a set of numbers or of a random variable.^[1]

It may also be defined as the arithmetic mean of the squares of the deviations between a set of numbers and a reference value (e.g., may be a mean or an assumed mean of the data),^[2] in which case it may be known as mean square deviation.When the reference value is the assumed true value, the result is known as mean squared error.

A typical estimate for the sample variance from a set of sample values

x _{i} uses a divisor of the number of values minus one, n-1, rather than n as in a simple quadratic mean, and this is still called the "mean square" (e.g. in analysis of variance):s ^{2} _{i - \bar{x})}

The second moment of a random variable,

E(X ^{2} ) is also called the mean square.The square root of a mean square is known as the root mean square (RMS or rms), and can be used as an estimate of the standard deviation of a random variable.

Notes and References

1. Web site: Noise and Noise Rejection . engineering.purdue.edu/ME365/Textbook/chapter11 . 6 January 2020.
2. Web site: OECD Glossary of Statistical Terms . oecd.org . 6 January 2020.