Measures of Central Location

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.