Question

Income and education level Each March, the Bureau of Labor Statistics compiles an Annual Demographic Supplement to its monthly Current Population Survey. Data on about $71,067$individuals between the ages of 25 and 64 who were employed full-time were collected in one of these surveys. The parallel boxplots compare the distributions of income for people with five levels of education. This figure is a variation of the boxplot idea: because large data sets often contain very extreme observations, we omitted the individuals in each category with the top 5% and bottom 5% of incomes. Also, the whiskers are drawn all the way to the maximum and minimum values of the remaining data for each distribution.

Use the graph to help answer the following questions.

a. What shape do the distributions of income have?

b. Explain how you know that there are outliers in the group that earned an advanced degree.

c. How does the typical income change as the highest education level reached increases? Why does this make sense?

d. Describe how the variability in income changes as the highest education level reached increases.

Short answer

a. Shape is right skewed.

b. Upper whisker of box plot "Advanced" is more than one and half times the width of box in box plot.

c. The income looks to increase as the highest education level increases.

d. The variability increases.

Step-by-step solution

Given Information

It is given that:

Shape of distribution of Income

Observations are:

• All five of distributions are right, skewed, as box in figure lie near bottom between two whiskers and the line in box of box plots lie closest to bottom of box.

To explain outliers in group that earned advanced degree

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

Third quartile shows by top of box plot and first quartile shows bottom of box where inner quartile range is showed by width of box.

Upper whisker of box plot "advanced" is more than $1.5$times width of box in box plot and hence it requires to contain at least one outlier.

To explain typical income change as the highest education level reached increases.

Income appears as highest education level increases. It is because box plot lies higher if level of education is higher. It makes sense as higher the degree, more money you make.

Effect on Variability

Variability is showed by width between whiskers of box plot.

Width between whiskers increases as highest education level increases. Hence, variability increases as highest education level increases.