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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