Question

Pulse rates Refer to Exercise 88.

(a) Find the range of the pulse rates for all 19 students and the range of the pulse rates excluding the student with the medical issue.

(b) Explain what part (a) suggests about using the range as a measure of variability for a distribution of quantitative data.

Short answer

Part (a) 52, 36

Part (b) When the dataset contains outliers, the range is an unreliable measure of variability.

Step-by-step solution

Part (a) Step 1. Given information.

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

Part (a) Step 2. Find the range.

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

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

Part (b) Step 1. Explanation.

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.