# Freedman–Diaconis rule

In statistics, the Freedman–Diaconis rule can be used to select the width of the bins to be used in a histogram. It is named after David A. Freedman and Persi Diaconis.

For a set of empirical measurements sampled from some probability distribution, the Freedman-Diaconis rule is designed to minimize the difference between the area under the empirical probability distribution and the area under the theoretical probability distribution.[clarification needed]

The general equation for the rule is:

${\text{Bin width}}=2\,{{\text{IQR}}(x) \over {\sqrt[{3}]{n}}}$ where $\operatorname {IQR} (x)$ is the interquartile range of the data and $n$ is the number of observations in the sample $x.$ ## Other approaches

Another approach is to use Sturges' rule: use a bin so large that there are about $1+\log _{2}n$ non-empty bins (Scott, 2009). This works well for n under 200, but was found to be inaccurate for large n. For a discussion and an alternative approach, see Birgé and Rozenholc.