Standard deviation is a measure of how much the realizations of a random variable are dispersed around its mean. It is equal to the square root of variance.

A precise definition follows.

Definition
Let
be a random variable and let
be
its variance. The **standard deviation** of
,
which is usually denoted by
or by
,
is the square root of its
variance:

Standard deviation is often deemed easier to interpret than variance, because it is expressed in the same units as the random variable . For example, if is the height of an individual extracted at random from a population, measured in inches, thenis also expressed in inches, butis expressed in squared inches; as a consequence, also the variance is expressed in squared inches, but the standard deviationis again expressed in inches.

More details about the standard deviation can be found in the lecture entitled Variance.

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