# Statistics and Probability Dictionary

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### Variance

The variance is a numerical value used to indicate how widely individuals in a group vary. If individual observations vary greatly from the group mean, the variance is big; and vice versa.

It is important to distinguish between the variance of a population and the
variance of a sample. They have different notation, and they are computed
differently. The variance of a population is denoted by σ^{2};
and the variance of a sample, by *s*^{2}.

The variance of a population is defined by the following formula:

σ^{2} = Σ ( X_{i} - X )^{2} / N

where σ^{2} is the population variance,
X
is the population mean, X_{i} is the *i*th element
from the population, and N is the number of elements in the population.

The variance of a sample is defined by slightly different formula:

*s*^{2} = Σ (
x_{i} - x )^{2} / ( n - 1 )

where *s*^{2} is the sample variance, x is
the sample mean, x_{i} is the *i*th element from the sample, and n
is the number of elements in the sample. Using this formula, the variance of the sample
is an unbiased estimate of the variance of the population.

And finally, the variance is equal to the square of the standard deviation.

See also: | Statistics Tutorial: Measures of Variability | AP Statistics Tutorial: Measures of Variability | Random Variable Attributes |