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A measure of spread of a distribution. It is equal to the mean of the squared distance of the variable from its mean:

Var(x) = 1 n ∑ x  ( x − - x   ) 2 ,

where n is the number of possible values of x, and [(x)] means the mean of x.
It is often written σ² , where σ is the standard deviation.
It can be shown that the variance of X is equal to [((x²))] − ( [(x)])² , where [((x²))] means the mean of x².

A random variable X has variance

var X = E(X− E X)2 = E X2 − ( E X)2.

The standard deviation of X is + √{ var X} .
See also covariance.