# Freedman–Diaconis rule

In statistics, the **Freedman–Diaconis rule** can be used to select the size of the bins to be used in a histogram.^{[1]} It is named after David A. Freedman and Persi Diaconis.

For a set 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:

where is the interquartile range of the data and is the number of observations in the sample

## Other approaches

Another approach is to use *Sturges' rule*: use a bin so large that there are about 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]}

## References

**^**Freedman, David; Diaconis, Persi (December 1981). "On the histogram as a density estimator:*L*_{2}theory" (PDF).*Probability Theory and Related Fields*. Heidelberg: Springer Berlin.**57**(4): 453–476. doi:10.1007/BF01025868. ISSN 0178-8051. Retrieved 2009-01-06.**^**Scott, D.W. (2009). "Sturges' rule".*WIREs Computational Statistics*.**1**: 303–306. doi:10.1002/wics.35.**^**Hyndman, R.J. (1995). "The problem with Sturges' rule for constructing histograms" (PDF).**^**Birgé, L.; Rozenholc, Y. (2006). "How many bins should be put in a regular histogram".*ESAIM: Probability and Statistics*.**10**: 24–45. CiteSeerX 10.1.1.3.220 . doi:10.1051/ps:2006001.