Chapter 13.4, Problem 15HP

(a)

To determine

To Find:The sets of scores that satisfy the data.

Answer to Problem 15HP

  $\{28,29,29,31,32,37,38,39,40,41,43,45,48\}$

Explanation of Solution

Given: Total students = $13$, minimum= $28$ , lower quartile score= $30$ , median= $38$ , upper quartile = $42$ , maximum= $48$

Here

There are $13$students

Then

The set of data which satisfies the given minimum= $28$ , lower quartile score= $30$ , median= $38$ , upper quartile = $42$ , maximum= $48$ is

  $\{28,29,29,31,32,37,38,39,40,41,43,45,48\}$

(b)

To determine

To Find: Number of students in the class if there are six students having score in the range of $38-42$

  $$$$

Answer to Problem 15HP

  $21$ Students

Explanation of Solution

Given: minimum= $28$ , lower quartile score= $30$ , median= $38$ , upper quartile == $42$ , maximum= $48$$$

Here total students are six

This means that including $38and42$ there is $4$ more students in the range.

But this constitutes the $25\%$ of the range

In box-and-whisker plot

The lower quartile, median, upper quartile in between these points will be $25\%$

Thus

Number of students in the class having score in the range of $38-42$ are

  $\begin{array}{l}=LE+4students+LQ+4students+ME+4students+UQ+4students+UE\\ =1+4+1+4+1+4+1+4+1\\ =21\end{array}$

Hence there are total $21$ students.