Question

Quiz grades Refer to Exercise 87.

(a) Find the median of Joey’s first 14 quiz grades.

(b) Find the median of Joey’s quiz grades after his unexcused absence. Explain why the 0 quiz grade does not have much effect on the median.

Short answer

Part (a) 85

Part (b) 84, resistant property of the median

Step-by-step solution

Part (a) Step 1. Given information.

The given grades are:

Part (a) step 1. Find the median 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

As we know that median is the middle value of a data set. As the given set is even, the median will be the average of the two middle values (7th and 8th) of this sorted data:

$$\begin{gathered} M=\frac{84+86}{2} \\ =\frac{170}{2} \\ =85 \end{gathered}$$

Part (b) Step 1.  Find the median of Joey’s quiz grades after his unexcused absence.

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

Arrange the given grades from smallest to largest:

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

Median is:

$M=84$

Median is a resistant measure of center, the reason is median is not strongly influenced by the extreme observations. Therefore, the resistant property of the median is followed here.