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Sturges' rule

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Abstract Histograms are among the most important graphical objects in statistical practice, providing a consistent estimate of any continuous density function with very few assumptions. Restricting attention to bins of equal width, the histogram is sometimes presented as a frequency chart or normalized to be a true density. The construction of a histogram may be specified by either its bin width or by the number of bins. Sturges' rule gives a number‐of‐bins formula. The formula was the first rule given in the literature and is still widely implemented in software today. This article reviews the underlying rationale for the rule and indicates when it is most appropriate to use in practice. Copyright © 2009 John Wiley & Sons, Inc. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Density Estimation

Two examples of Sturges' rule in action with normal data and sample sizes n = 210 and n = 220 with 11 and 21 bins, respectively. The points along the x‐axes depict the support intervals, (a, b), of the frequency charts.

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Example of three rules on a normal sample of size 106. The sample range is (−4.93, 4.76). The number of bins given by Sturges' rule, the Terrell–Scott rule, and Scott's rule are 21, 126, and 277, respectively. The graph does not display the full extent of the histogram, and the histograms are displaced vertically for clarity. The true normal density is superimposed as a dotted line.

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(Left) Bin width for standard normal data as a function of sample size for Sturges' rule (solid line) and Scott's rule (dashed line). (Right) Number of bins as a function of sample size for Sturges' rule (solid line) and over the oversmoothed density (dashed line).

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