91Ó°ÊÓ

The given data about pulse rate is shown below:

71, 104, 76, 88, 78, 71, 68, 86, 70, 90, 74, 76, 69, 68, 88, 96, 68, 82, 120

The range formula is:

$\mathrm{Range}=\mathrm{Maximum}\mathrm{value}-\mathrm{Minimum}\mathrm{value}$

Arrange the given pulse rates from smallest to largest:

68, 68, 68, 69, 70, 71, 71, 71, 74, 76, 76, 78, 82, 86, 88, 88, 90, 96, 104, 120

$$\begin{gathered} \mathrm{Range}=120-68 \\ =52 \end{gathered}$$

After excluding students with medical issues.

Data for range after excluding the student with medical issues having a pulse rate of 120: 68, 68, 68, 69, 70, 71, 71, 71, 74, 76, 76, 78, 82, 86, 88, 88, 90, 96, 104

$$\begin{gathered} \mathrm{Range}=104-68 \\ =36 \end{gathered}$$

Before excluding the student, the range was 52, and after the excluding (when the outlier 120 is excluded), the range was 36.

This indicates that outliers have a considerable influence on the range (because of the large differences between the two ranges) and that the range is not resistant to outliers.

As a result, the range is an unreliable measure of variability, particularly when the sample contains outliers.