Most statistical packages use Sturges’ rule (or an extension of it) for selecting the number of classes when constructing a histogram. Sturges’ rule is also widely recommended in introductory statistics textbooks. It is known that Sturges’ rule leads to oversmoothed histograms, but Sturges’ derivation of his rule has never been questioned. In this note, I point out that the argument leading to Sturges’ rule is wrong.

It is well known that major strength of non-parametric regression function estimation breaks down when correlated errors exist in the data. Positively (negatively) correlated errors tend to produce undersmoothing (oversmoothing).