When Is it Preferable to Estimate Population Percentiles From a Set of Classes Rather Than From the Raw Data?

Abstract

For estimating percentiles of a distribution from a sample, it turns out that in many cases the observed percentiles provide better estimates when they are based on grouped data than when based on the raw data. This is the case especially when the data set is relatively small and the population distribution is not too skewed or heavy-tailed. This fact is surprising and contrary to the general feeling. Applied statisticians and producers of calculators could take advantage of it by implementing a small program for estimating percentiles from grouped data within their calculators. Such a program is generally impracticable if one uses raw data, due to lack of memory space and length of computing time.