Measures of Central Location
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buttons.Measures of Variability
The Range
The first measure of variability that we discuss is the simplest.
Definition
The range of a data set is the number R defined by the formula
\(R=x_{\max }-x_{\min }\)
where \(x_{\max }\) is the largest measurement in the data set and \(x_{\min }\) is the smallest.
Example 10
Find the range of each data set in Table 2.1 "Two Data Sets".
Solution:
For Data Set I the maximum is 43 and the minimum is 38, so the range is \(R=43-38=5\).
For Data Set II the maximum is 47 and the minimum is 33, so the range is \(R=47-33=14\).
The range is a measure of variability because it indicates the size of the interval over which the data points are distributed. A smaller range indicates less variability (less dispersion) among the data, whereas a larger range indicates the opposite.