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.[1] The general equation for the rule is:

\text{Bin size}=2\, { \text{IQR}(x) \over{ \sqrt[3]{n} }}\;

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).[2] This works well for n under 200, but was found to be inaccurate for large n.[3] For a discussion and an alternative approach, see Birgé and Rozenholc.[4]


  1. ^ Freedman, David; Diaconis, Persi (December 1981). "On the histogram as a density estimator: L2 theory" (PDF). Probability Theory and Related Fields (Heidelberg: Springer Berlin) 57 (4): 453–476. ISSN 0178-8051. Retrieved 2009-01-06. 
  2. ^ Scott, D.W. (2009). "Sturges' rule". WIREs Computational Statistics 1: 303–306. doi:10.1002/wics.35. 
  3. ^ Hyndman, R.J. (1995). "The problem with Sturges’ rule for constructing histograms" (PDF). 
  4. ^ Birgé, L.; Rozenholc, Y. (2006). "How many bins should be put in a regular histogram". ESAIM: Probability and Statistics 10: 24–45. doi:10.1051/ps:2006001.