Chapter PI, Problem 21RE

(a)

To determine

To make an appropriate plot and describe the distribution of the ratios.

Explanation of Solution

In the question it is given the table of the arm and nose measurements of the girls and also the arm is to nose ratio for this. Thus, the appropriate plot for this graph will be as:

Thus, as we look at the histogram above, we can say that the arm/nose ratio is on the horizontal axis. We can see that the distribution is left skewed as the bars at the left end are lower than of the right end bars. Also the center of the distribution is about $15$ . Also it has an outlier between $11\text{ and 12}$ .

(b)

To determine

To summarize the ratios numerically, choosing appropriate measure of center and spread.

Answer to Problem 21RE

The appropriate measure of the center and spread is the mean and the standard deviation.

Explanation of Solution

In the question it is given the table of the arm and nose measurements of the girls and also the arm is to nose ratio for this. Thus, the appropriate measure of the center and spread is the mean and the standard deviation. Even though the distribution is somewhat left skewed as we look at the histogram. Thus, the mean is about to be at $15$ and the standard deviation is about to be at $1.25$ .

(c)

To determine

To explain is the ratio of $9.3$ for the statue of the Liberty unrealistically low.

Answer to Problem 21RE

Yes, it is.

Explanation of Solution

In the question it is given the table of the arm and nose measurements of the girls and also the arm is to nose ratio for this. Thus, the ratio of $9.3$ for the statue of the Liberty unrealistically low because $11.8$ is already an outlier and $9.3$ is more than $4.5$ three standard deviation below the mean. So, it is a very low outlier.