Chapter 1.3, Problem 119E

(a)

To determine

To find: the shape of the distribution of income has.

Answer to Problem 119E

Right skewed

Explanation of Solution

Given:

  

By seeing the figure, it is observe that all five of the distributions of income are right skewed, because the box of the box plots are lying near the bottom between the two whiskers (which associates with small values) and the lines in the box of the box plots lie closest to the bottom of the box.

(b)

To determine

To Explain: that there are outliers in the group that earned an advanced degree.

Answer to Problem 119E

The upper whisker of the box plot “Advanced” is more than one and half times the width of the box in the box plot.

Explanation of Solution

Given:

  

Outliers are observations that are more than one and half times the IQR above $Q_3$ or below $Q_1$ .

The third quartile $Q_3$ is shows by the top of the box in the box plot and the 1^st quartile $Q_1$ is shows by the bottom of the box in the box plot, where the inter quartile range is showed by the width of the box.

It is observed that the upper whisker of the box plot “Advanced” is more than 1.5 times the width of the box in the box plot and therefore the data set “Advanced” requires to contain at least one outlier (as it will contain a data value that is more than one and half IQR above $Q_3$ .

(c)

To determine

To Explain: that the typical income change as the highest education level reached increases.

Answer to Problem 119E

The income looks to increase as the highest education level increases

Explanation of Solution

Given:

  

It is observed that the income appears as the highest education level increases; the reason is that the box plot lies higher if the education level is higher. This also makes sense, the reason is that the higher your degree, the more money you tend to make.

(d)

To determine

To Explain: the variability in income changes as the highest education level reached increases.

Answer to Problem 119E

Variability increases

Explanation of Solution

Given:

  

The variability of the income at an education level is showed by the width between the whiskers of the box plot. It is observed that the width between the whiskers increases as the highest education level increases, which means that the variability increases as the highest education level increases.