Chapter PI, Problem 24RE

(a)

To determine

To find a five-number summary for McGwire’s career.

Answer to Problem 24RE

  $\begin{array}{l}\text{Minimum}=3\\ \text{Maximum}=70\\ \text{1st quartile}=27.25\\ \text{3nd quartile}=49.75\\ IQR=22.50\\ \text{Median}=36\end{array}$

Explanation of Solution

In the question, the home run totals for each season McGwire played and Babe Ruth played is given. Now, we will calculate the five-number summary through the calculator $\text{TI}-89$ . Thus, if we have to compute the summary statistics then press $\text{F4}$ , that is Calc. and then input the name of the list using VAR-LINK and then press enter. The summary statistics will appear/ thus, the result will be:

  $\begin{array}{l}\text{Minimum}=3\\ \text{Maximum}=70\\ \text{1st quartile}=27.25\\ \text{3nd quartile}=49.75\\ IQR=22.50\\ \text{Median}=36\end{array}$

(b)

To determine

To explain do any of his seasons appear to be outliers.

Answer to Problem 24RE

Yes, there is an outlier.

Explanation of Solution

In the question, the home run totals for each season McGwire played and Babe Ruth played is given. Yes, for his seasons there appear to be outliers as on the point $3,9,9$ appear to be outlier because they are all a group away from the rest of the data and they appear to be very small from the other points of the home run.

(c)

To determine

To omit these values and make a parallel boxplots comparing McGwire’s career to Babe Ruth’s.

Explanation of Solution

In the question, the home run totals for each season McGwire played and Babe Ruth played is given. Thus, the parallel boxplots comparing McGwire’s career to Babe Ruth’s is as follows:

(d)

To determine

To write a few sentences comparing the two sluggers.

Explanation of Solution

In the question, the home run totals for each season McGwire played and Babe Ruth played is given. We can say about the comparing the two sluggers that McGwire and Ruth have the same minimum home runs and McGwire has a median of $42$ and Ruth has a higher median with a value of $46$ . McGwire has a maximum of $70$ and Ruth has a maximum of $60$ .

(e)

To determine

To create a side-by-side stem and leaf display comparing the career of the two players.

Explanation of Solution

In the question, the home run totals for each season McGwire played and Babe Ruth played is given. Thus, the stem and leaf display comparing the career of the two players are as follows:

For McGwire:

Frequency	Stem	Leaf
2	2	2 9
5	3	2 2 3 9 9
2	4	2 9
2	5	2 8
1	6	5
1	7	0
13

For Ruth:

Frequency	Stem	Leaf
2	2	2 5
2	3	4 5
7	4	1 1 6 6 6 7 9
3	5	4 4 9
1	6	0
15

(f)

To determine

To find out what aspects of the distributions are apparent in the stem and leaf displays that did not clearly show in the boxplots.

Explanation of Solution

In the question, the home run totals for each season McGwire played and Babe Ruth played is given. If we look at the data McGwire’s data looks skewed using the stem and leaf plot and Ruth’s data looks fairly symmetric as given in the part (e) above. And we cannot see that in the boxplots of the two in part (c).