In descriptive statistics, the range of a set of data is size of the narrowest interval which contains all the data. It is calculated as the difference between the largest and smallest values (also known as the sample maximum and minimum). It is expressed in the same units as the data.

The range provides an indication of statistical dispersion. Closely related alternative measures are the Interdecile range and the Interquartile range.

For n independent and identically distributed continuous random variables X₁, X₂, ..., X_n with the cumulative distribution function G(x) and a probability density function g(x), let T denote the range of them, that is, T= max(X₁, X₂, ..., X_n)- min(X₁, X₂, ..., X_n).

The range, T, has the cumulative distribution function

Gumbel notes that the "beauty of this formula is completely marred by the facts that, in general, we cannot express G(x + t) by G(x), and that the numerical integration is lengthy and tiresome."

If the distribution of each X_i is limited to the right (or left) then the asymptotic distribution of the range is equal to the asymptotic distribution of the largest (smallest) value. For more general distributions the asymptotic distribution can be expressed as a Bessel function.

The mean range is given by

where x(G) is the inverse function. In the case where each of the X_i has a standard normal distribution, the mean range is given by