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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 variance is small and if many values are far from the population mean then the population variance is large.
The positive square root of the population variance is equal to the population standard deviation.
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 variance is not known. The population variance may be estimated by taking a random sample of values from the population, calculating the sample variance and using this value as an estimate of the population variance.
The population variance is a number representing the spread of a population and is therefore an example of a population parameter.
The square of the population standard deviation is equal to the population variance, so σ2 (sigma squared) is the most common symbol for the population variance.
See: measure of spread, variance, variance (of a discrete random variable)
Curriculum achievement objectives references
Statistical investigation: Levels (7), (8)
