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The range of a data set is the easiest measure of dispersion to calculate. Range is defined as

(2.5.5)

The range is not an efficient measure of dispersion because it takes into consideration only the largest and the smallest values and none of the remaining observations. For example, if a data set has 100 distinct observations, it uses only two observations and ignores the remaining 98 observations. As a rule of thumb, if the data set contains 10 or fewer observations, the range is considered a reasonably good measure of dispersion. For data sets containing more than 10 observations, the range is not considered to be an efficient measure of dispersion.

Example 2.5.9 (Tensile strength) The following data gives the tensile strength (in psi) of a sample of certain material submitted for inspection. Find the range for this data set:

8538.24, 8450.16, 8494.27, 8317.34, 8443.99, 8368.04, 8368.94, 8424.41, 8427.34, 8517.64

Solution: The largest and the smallest values in the data set are 8538.24 and 8317.34, respectively. Therefore, the range for this data set is