Business Mathematics and Statistics · Ch 9 — Measures of Dispersion
Range and Coefficient of Range
Range and Coefficient of Range
The Range is the simplest possible measure of dispersion — the difference between the largest and the smallest value in a data set.
Range
where is the largest observation and is the smallest observation in the series. For a grouped/continuous distribution, is taken as the upper limit of the highest class and as the lower limit of the lowest class.
Because Range depends on only the two extreme values, it is unstable — it ignores every other observation entirely, so a single unusually high or low value can distort it badly, and it always grows (or stays the same) as more data is added, never shrinks. Its major merit is that it is extremely quick to compute and easy to understand, which is why it is still widely used for a first, rough impression of variability — for instance, a quality inspector doing a quick daily check of a machine's output range before running any deeper analysis.
Being an absolute measure (in the same unit as the data), Range cannot be used to compare the variability of two series recorded in different units or of very different average size. The Coefficient of Range fixes this by expressing the range relative to the total of the two extremes:
Coefficient of Range
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The difference between the largest () and smallest () values in a data set: . The simplest, but least stable, measure of dispersion, since it de …
The range expressed relative to the sum of the two extreme values, — a unit-free relative measure allowing fair c …