New class width rule for continuous frequency tables

Abstract

The most significant parameter which must be determined before constructing a frequency table or a histogram is the number of classes or class width. Choosing the appropriate number of classes or class remains a long-lasting problem in statistics. Apart from the rules of thumb several more sophisticated rules were reported in the literature. However, none of them has been proven to be better in all situations. In this research, we proposed a new class width rule which can be used when building a frequency table or a histogram. The new class width rule is compared with nine existing classification rules, Sturges, Scott, Freedman and Diaconis, Doane, Terrel and Scott, Cencov, Cochran, Square root, and Rice rules, using the root mean-squared-error (RMSE). The accuracy of the classification rules is assessed using simulations from normal, uniform, exponential, log-normal, and gamma distributions, and also real data. The findings indicated that the proposed rule outperformed the other binning rules for simulations using normal, exponential, log-normal, and gamma distributions. Meanwhile, the square root rule performed better relative to the other classification rules for simulations from the uniform distribution. Comparison using real data showed that the proposed rule performed better than the other classification rules.