Chapter PI, Problem 38RE

(a)

To determine

To find the five-number summary.

Answer to Problem 38RE

  $\begin{array}{l}\text{Minimum}=-9\\ \text{First quartile}=1\\ \text{Median}=4\\ \text{Third quartile}=9.5\\ \text{Maximum}=25\end{array}$

Explanation of Solution

It is given in the question that the stem and leaf diagram is given which displays profits as a percent of sales for $29$ of the Forbes $500$ largest U.S. corporations. 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:

  $\begin{array}{l}\text{Minimum}=-9\\ \text{First quartile}=1\\ \text{Median}=4\\ \text{Third quartile}=9.5\\ \text{Maximum}=25\end{array}$

(b)

To determine

To draw a boxplot for these data.

Explanation of Solution

It is given in the question that the stem and leaf diagram is given which displays profits as a percent of sales for $29$ of the Forbes $500$ largest U.S. corporations. Thus, the boxplot for these data will be as:

(c)

To determine

To find the mean and standard deviation.

Answer to Problem 38RE

  $\begin{array}{l}\text{Mean}=4.72\\ \text{SD}=7.55\end{array}$

Explanation of Solution

It is given in the question that the stem and leaf diagram is given which displays profits as a percent of sales for $29$ of the Forbes $500$ largest U.S. corporations. Now, we will calculate the mean and the standard deviation 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:

  $\begin{array}{l}\text{Mean}=4.72\\ \text{SD}=7.55\end{array}$

(d)

To determine

To describe the distribution of profits for these corporations.

Explanation of Solution

It is given in the question that the stem and leaf diagram is given which displays profits as a percent of sales for $29$ of the Forbes $500$ largest U.S. corporations. Thus, we can say about this distribution by looking at the information given and the histogram and the stem and leaf diagram for these data that this distribution is uni-modal. And the distribution is slightly skewed to the right as more values are there.