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A measure of spread for a population distribution of a numerical variable that determines the degree to which the values differ from the population mean. If many values are close to the population mean then the population standard deviation is small and if many values are far from the population mean then the population standard deviation is large.
The square of the population standard deviation is equal to the population variance.
In many real situations the collection of all values from a population is not available, for a variety of reasons. For example, the collection may be infinite or some objects or individuals may not be accessible. In such cases the value of the population standard deviation is not known. The population standard deviation may be estimated by taking a random sample of values from the population, calculating the sample standard deviation and using this value as an estimate of the population standard deviation.
The population standard deviation is a number representing the spread of the population distribution and is therefore an example of a population parameter.
The Greek letter σ (sigma) is the most common symbol for the population standard deviation.
See: measure of spread, population variance, standard deviation, standard deviation (of a discrete random variable)
Curriculum achievement objectives references
Statistical investigation: Levels (7), (8)
