Freedman-Diaconis rule

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In statistics, the Freedman-Diaconis rule is used to specify the size of the bins to be used in a histogram; which will tend to smooth the data. The general equation for the rule is:

<math>\mbox{Bin size}=2\, \mbox{IQR}(x) N^{-1/3} \;</math>

where

<math>x \;</math> is the data

<math>\mbox{IQR} \;</math> is the interquartile range of the data

<math>N \;</math> is the number of observations in the sample <math>x. \; </math>

[edit] Sturges' rule

Another approach is the use Sturges' rule: use a bin so large that there are about <math>1+\log_2n</math> non-empty bins.

For a thousand items, the Freedman-Diaconis rule would suggest about 40 bars; Sturges, 11.

[edit] Reference

• Freedman D and Diaconis P (1981). On the histogram as a density estimator:<math>L_2</math> theory. Probability Theory and Related Fields. 57(4): 453-476