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Standard deviation

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.

Definition

A precise definition follows.

Definition Let X be a random variable and let [eq1]be its variance. The standard deviation of X, which is usually denoted by [eq2] or by [eq3], is the square root of its variance:[eq4]

Interpretation

Standard deviation is often deemed easier to interpret than variance, because it is expressed in the same units as the random variable X. For example, if X is the height of an individual extracted at random from a population, measured in inches, then[eq5]is also expressed in inches, but[eq6]is expressed in squared inches; as a consequence, also the variance [eq7]is expressed in squared inches, but the standard deviation[eq8]is again expressed in inches.

More details

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

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