Multiple Choice Select the best answer for Exercises 123–126.

Which of the following boxplots best matches the distribution shown in the histogram?

The given histogram is:

We can see that the histogram's distribution is bimodal, with two beaks on each side, and symmetric, with the histogram on the, left 15.5 mirroring the histogram on the right of 5.5.

As the histogram has no gaps, there are no outliers.

(a) This boxplot is the best match because it is roughly symmetric (as the box of the boxplot lies in the middle between the endpoints and the line in the box of the boxplot lies roughly in the middle of the box) and because the box of the boxplot is very wide (as most of the values lie on each side of the histogram and thus the first line in the box of the boxplot lies roughly in the middle of the box).

(b) This boxplot isn't a good fit because the box isn't very wide, although we'd expect a wide boxplot because the data has a lot of variability due to the two modes on either side of the histogram.

(c) This boxplot isn't a good fit because the box isn't very wide, although we would expect a wide boxplot because the data has a lot of variability due to the two modes on either side of the histogram.

Furthermore, this boxplot has two outliers (two dots in the boxplot), but the histogram did not appear to have any outliers. This plot isn't particularly interesting.

(d) This boxplot is not a good match because the boxplot is not symmetric because the boxplot's box sits to the left between the boxplot's endpoints.

(e) This boxplot isn't a good match since the boxplot isn't symmetric, with the box's box lying to the right between the boxplot's endpoints.