Chapter 1.3, Problem 126E

To determine

Boxplot that matches best with the distribution shown in the histogram.

Answer to Problem 126E

Boxplot (a) matches best with the distribution shown in the histogram.

Explanation of Solution

Given information:

  

Note that

The distribution in the histogram:

• Symmetric, as the histogram to the left of 5.5 is the mirror image of the histogram to the right of 5.5.
• No outliers, as there are no gaps in histogram.
• Bimodal, as the histogram contains two peaks, one on each side of the histogram.

In boxplot (a), since the boxplot is roughly symmetric and the box of the boxplot is very wide.

Thus, the boxplot seems to be the best match for the distribution.

In boxplot (b), since the box of the boxplot is not very wide and the data has a large amount of variability due to two modes that are on either side of the histogram, we are expecting a wider boxplot. Thus, this boxplot is not a very good match.

In boxplot (c), since the box of the boxplot is not very wide and wide boxplot is expected as the data has a large amount of variability due to two modes that are on either side of the histogram. Moreover, the boxplot contains two outliers and the histogram did not appear to contain outliers. Thus, this boxplot is not a very good match.

In boxplot (d), since the boxplot is not symmetric as the box of the boxplot lies to the left between the endpoints of the boxplot. Thus, this boxplot is not a very good match.

In boxplot (e), since the boxplot is not symmetric as the box of the boxplot lies to the right between the endpoints of the boxplot. Thus, this boxplot is not a very good match.