Variance

The variance of a data set is a measure of how "spread out" the data points are in general.

Formula

Population

For a dataset $X = \{ x_1, x_2, x_3, \dots, x_n \}$ with mean $\overline{x}$ the formula for variance if $X$ is a population is $V = \frac{1}{n}\sum_{i=1}^n (x_i - \overline{x})^2.$ Additionally, $V = \sigma^2$ where $\sigma$ is the population standard deviation.

Sample

Because of Bessel's correction the variance if $X$ is a sample is calculated according to the slightly different formula $V = \frac{1}{n-1}\sum_{i=1}^n (x_i - \overline{x})^2.$

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Variance

Formula

Population

Sample