Sturges' Rule

Sturges' Rule estimates an approximate number of classes for a grouped frequency table or histogram from the number of observations. The method, published by Herbert A. Sturges in 1926, uses the binary logarithm of sample size:

k ≈ 1 + log2(n)
  ≈ 1 + 3.321928 × log10(n)

Here n is the number of observations and k is the approximate number of classes. The estimate is converted to a positive integer when constructing a grouped table. The number of classes therefore grows logarithmically with sample size.

Role in constructing a distribution

Sturges' rule determines a class-count estimate; the class limits are established separately. The procedure first identifies the sample minimum and maximum, then uses their range and the selected number of classes to calculate an interval width. The resulting groups support counting observations and constructing a numerical summary of the distribution.

Scott's method bases class width on standard deviation, while the Freedman–Diaconis method uses the interquartile range. These approaches incorporate variation within the data, whereas Sturges' rule starts from sample size. The choice influences how much distributional detail appears in the table or histogram.

In the December 2014 Frequency Table Generation project, the 120-observation example is organized into seven classes using a decimal-logarithm expression with coefficient 3.3. Frequency Table defines the class counts and cumulative frequencies; Probability and Statistics provides the broader statistical context.