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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.
It may also be defined as the arithmetic mean of the squares of the deviations between a set of numbers and a reference value , 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 {\displaystyle 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" :
The second moment of a random variable, E {\displaystyle E} is also called the mean square.The square root of a mean square is known as the root mean square , and can be used as an estimate of the standard deviation of a random variable.