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quadratic variance, standard deviation, of quantities from

The square root of the expression

 (*)

The quadratic deviation takes its smallest value when , where is the arithmetic mean of :

In this case the quadratic deviation serves as a measure of the variance (cf. Dispersion) of the quantities . Also used is the more general concept of a weighted quadratic deviation:

where the are the so-called weights associated with . The weighted quadratic deviation attains its smallest value when is the weighted mean:

In probability theory, the quadratic deviation of a random variable (from its mathematical expectation) refers to the square root of its variance: .

The quadratic deviation is taken as a measure of the quality of statistical estimators and in this case is referred to as the quadratic error.