Question

Quiz gradesRefer to Exercise 87.

(a) Find the range of Joey’s first 14 quiz grades and the range of Joey’s quiz grades after his unexcused absence.

(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) 24 and 98

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 is:

86, 84, 91, 75, 78, 80, 74, 87, 76, 96, 82, 90, 98, 93

Part (a) Step 2. Find the range of Joey’s first 14 quiz grades.

Arrange the given grades from smallest to largest:

74, 75, 76, 78, 80, 82, 84, 86, 87, 90, 91, 93, 96, 98

The range before absence:

$$\begin{gathered} =\mathrm{Maximum}\mathrm{value}-\mathrm{Minimum}\mathrm{value} \\ =98-74 \\ =24 \end{gathered}$$

Range after the absence:

0, 74, 75, 76, 78, 80, 82, 84, 86, 87, 90, 91, 93, 96, 98

$$\begin{gathered} \mathrm{Range}=98-0 \\ =98 \end{gathered}$$

Part (b) Explanation.

Before the absence, the range was 24, and after the absence (when the outlier 0 is added), the range was 98.

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.