Chapter 13.4, Problem 10PPS

(a)

To determine

Set of data having greater range.

Answer to Problem 10PPS

Women have largest range.

Explanation of Solution

Given data:

The double box and whisker plot of 2004 Men`s and Women`s Olympic swimming team.

For men $Q_1=18,Q_2=21,Q_3=22$

For women $Q_1=21,Q_2=22,Q_3=26$

Calculation:

Women has the largest range as there are 13 players in swimming team.

Conclusion:

Women have largest range..

(b)

To determine

Number of outliers of the plotter of age in 2004 Men`s and Women`s Olympic swimming team

Answer to Problem 10PPS

There is only one Outlier.

Explanation of Solution

Given data:

The double box and whisker plot of 2004 Men`s and Women`s Olympic swimming team.

For men $Q_1=18,Q_2=21,Q_3=22$

For women $Q_1=21,Q_2=22,Q_3=26$

Formula used:

  $\begin{array}{l}IQR=Q_3-Q_1\\ Outlier\\ \max =Q_3+1.5IQR\\ \min =Q_1-1.5IQR\end{array}$

Calculation:

Outliers of men`s plotter graph

  $\begin{array}{l}IQR=22-18\\ =\text{4}\\ Outlier\\ \max =22+1.5\times 4\\ =\text{28}\\ \min =18-1.5\times 4\\ =\text{12}\end{array}$

As there is minimum value is 15 so only max outlier is in men`s plot

Outlier of women`s plot

  $\begin{array}{l}IQR=26-21\\ =\text{5}\\ Outlier\\ \max =26+1.5\times 5\\ =\text{33}\text{.5}\\ \min =21-1.5\times 5\\ =\text{13}\text{.5}\end{array}$

As plot min plot is 15 and max is 31 so there is no out lier in women`s plot

There is only one outlier in the plot.

Conclusion:

There is only one Outlier.

(c)

To determine

Percentage of team having women of 22 year or younger.

Answer to Problem 10PPS

50% women are 22 years and younger.

Explanation of Solution

Given data:

The double box and whisker plot of 2004 Men`s and Women`s Olympic swimming team.

For men $Q_1=18,Q_2=21,Q_3=22$

For women $Q_1=21,Q_2=22,Q_3=26$

Calculation:

As the median line represent 50% of data so,

50% women are 22 year or younger in Olympic swimming teams.

Conclusion:

50% women are 22 years and younger.

(d)

To determine

Comparing age of men to women.

Answer to Problem 10PPS

Men are younger than women Olympic swimming team.

Explanation of Solution

Given data:

The double box and whisker plot of 2004 Men`s and Women`s Olympic swimming team.

For men $Q_1=18,Q_2=21,Q_3=22$

For women $Q_1=21,Q_2=22,Q_3=26$

Calculation:

In the Olympics men ages are varies from 15 -27 years whereas women`s team age varies from 18-31 years.

Conclusion:

Men are younger than women Olympic swimming team.