Question

Income in New England The following boxplots show the total income of 40 randomly chosen households each from Connecticut, Maine, and Massachusetts, based on U.S. Census data from the American Community Survey. Compare the distributions of annual incomes in the three states.

Short answer

The Connecticut distribution appears to be fairly symmetric, whereas the Maine and Massachusetts distributions appear to be biassed to the right.

Massachusetts has the highest centre, while Maine has the lowest.

Massachusetts has the biggest spread, and Maine has the lowest.

There is one outlier in each of the Main and Massachusetts distributions, but there appear to be none in the Connecticut distribution.

Step-by-step solution

Step 1. Given information.

The given information is:

Step 2. Compare the distributions of annual incomes in the three states.

The box is about the midway between the whiskers, the Connecticut distribution appears to be roughly symmetric. Because the box of the boxplot lies to the left between the whiskers, the Maine and Massachusetts distributions are skewed to the right.

The vertical line in the box of the boxplot (which represents the median) represents the centre of the distributions. We then see that the Massachusetts distribution centre appears to be the highest, while the Maine distribution centre looks to be the lowest.

The spread is represented by the distance between the boxplot's whiskers. Then we see that the Massachusetts distribution appears to have the widest spread, while the Maine distribution looks to have the narrowest spread.

We see that the lain and Massachusetts distributions each have one outlier (shown in the boxplot), whereas the Connecticut distribution appears to have none.