standard deviation
(symbol: SD) a measure of the variability of a set of scores or values within a group, indicating how narrowly or broadly they deviate from the mean. A small standard deviation indicates data points that cluster around the mean, whereas a large standard deviation indicates data points that are dispersed across many different values. The standard deviation is expressed in the same units as the original values in the sample or population studied, so that the standard deviation of a series of measurements of weight would be in pounds, for example. The standard deviation is equal to the square root of the variance. If a population of n values has a mean μ, then the standard deviation is
√[Σ(Xi – μ)2/n].
For a subset of the population, with a mean value X̄, the sample standard deviation is
√[Σ(Xi – X̄)2/(n – 1)];
that is, the divisor is (n – 1) rather than n. See also root mean square.