Freedman–Diaconis rule

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In statistics, the Freedman–Diaconis rule, named after David A. Freedman and Persi Diaconis, can be used to select the size of the bins to be used in a histogram. The general equation for the rule is:

\text{Bin size}=2\, \text{IQR}(x) n^{-1/3} \;

where \scriptstyle\operatorname{IQR}(x) \; is the interquartile range of the data and \scriptstyle n \; is the number of observations in the sample \scriptstyle x. \;

Other approaches[edit]

Another approach is to use Sturges' rule: use a bin so large that there are about \scriptstyle 1+\log_2n 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.