Range as a zoological character

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Abstract
The difference between maximum and minimum observed values of a variate, defined as observed range, is commonly used in zoology and paleontology as a measure of variation in species or other groups. In fact the range observed in a sample is not directly related to the range in a population and is never a valid estimate of the latter. The common procedure of comparing ranges observed in samples of different sizes is also incorrect and may be grossly misleading. Range is related in a complex way with the sizes of samples or populations and their standard deviations. To make ranges comparable with each other and to make them consistent estimates of a character of the population, it is necessary to estimate mean ranges for groups of some standard size, here proposed as 1000. Methods for calculating such estimates, called standard ranges, are given, as well as tests of their reliability. Empirical study confirms their validity. Standard ranges and related methods permit quick and simple tests involved in zoological comparisons. They are cruder than the best statistical methods but they involve much simpler calculations and may be easier to comprehend. They are valid within their defined limits and frequently save the labor of making more complicated tests.

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