A measure of the variation of empirical data or of a theoretical distribution. It is calculated by taking the average of the square of the difference between the data items and their mean (μ), that is the average square of the residual.

variance = ( Σ (x_{i }– μ)^{2} ) / N – where x_{i } is the i-th data item and N is the number of items

Often the mean of empirical data is estimated based on the data in a sample; in such cases the simple formula slightly underestimates the real value of the variance and instead the sum of squares is divided by N–1.

The variance is a square measure, which is not easy to interpret (for example the variance of people's height is in square metres). So, more often the standard deviation (s.d., σ) is given, which is the square root of the variance.

The variance is also typically less robust than other measures of variation such as interquartile range. However, variances have nice mathematical properties – they 'add up' – and so are heavily used.

Used on pages 24, 30, 50, 51, 81