Chapter 11.2, Problem 17E

(a)

To determine

To identify the shape of each distribution.

Answer to Problem 17E

Symmetric distribution

Explanation of Solution

Given information: Box-and-whisker plot.

Calculation:

It is a symmetric distribution. Because a symmetric graph forms a mirror image of itself when reflected in its vertical center line.

(b)

To determine

To describe which sales of representatives is more spread out.

Answer to Problem 17E

Sales B

Explanation of Solution

Given information: Box-and-whisker plot.

Formula Used:Range of the data= $max.-\min .$ and Interquartile range of the data = $Q_3-Q_1$

Calculation:

  

Representative A:

• As the range of the data: $max.-\min .$

So,

Range= $20-8$

Hence,

Range= $8$

• As the Interquartile range of the data = $Q_3-Q_1$

So,

Interquartile Range= $16-12$

Hence,

Interquartile Range= $4$

Representative B:

• As the range of the data: $max.-\min .$

So,

Range= $24-4$

Hence,

Range= $20$

• As the Interquartile range of the data = $Q_3-Q_1$

So,

Interquartile Range= $16-8$

Hence,

Interquartile Range= $8$

Sales of representatives B is more spread out than that of A.

Because range of the data of B is much greater than interquartile range of B.

(c)

To determine

To describe which representatives the single worst sales month during the year.

Answer to Problem 17E

Sales B

Explanation of Solution

Given information: Box-and-whisker plot.

Calculation:

  

• Representative A:

Median = 14

• Representative B:

Median = 10

Sales of representatives B had the single worst sales month during the year because its median is too small.