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Mean square

From Wikipedia, the free encyclopedia

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 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):

The second moment of a random variable, 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 when the random variable is zero-mean.

References

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  1. ^ "Noise and Noise Rejection" (PDF). engineering.purdue.edu/ME365/Textbook/chapter11. Retrieved 6 January 2020.
  2. ^ "OECD Glossary of Statistical Terms". oecd.org. Retrieved 6 January 2020.