Chapter 1.2, Problem 75E

a.

To determine

To know that do students who graduate from high school earn more money than students who do not and will it be appropriate to use frequency histograms instead of relative frequency histograms in this setting.

Answer to Problem 75E

No. it would not be appropriate to use frequency histograms instead of relative frequency histograms.

Explanation of Solution

Given a random sample of 371 U.S. residents aged 18 and older. The educational level and total personal income of each person were recorded. The data for the 57 non-graduates (No) and the 314 graduates (Yes) are displayed in the relative frequency histograms provided below:

  

  

It would not be appropriate to use frequency histograms instead of relative frequency histograms, because the two histograms do not use the same number of data values (as there are 314 graduates but only 57 non-graduates). Since these two histograms would then not be based on the same number of data values, we would not be able to compare the frequency histograms.

b.

To determine

To know that do students who graduate from high school earn more money than students who do not and to compare the distributions of total personal income for these two groups.

Answer to Problem 75E

Both distributions are skewed to the right.

The distribution of the nongraduates do not appear to contain any outliers, while the distribution of the graduates contains possible outliers.

The center of both distributions appears to be roughly between 0 and 10 thousand dollars.

The spread of the graduate distributions is greater than the spread for the nongraduate distribution.

Explanation of Solution

Given a random sample of 371 U.S. residents aged 18 and older. The educational level and total personal income of each person were recorded. The data for the 57 non-graduates (No) and the 314 graduates (Yes) are displayed in the relative frequency histograms provided below:

  

  

Both distributions are skewed to the right, because the highest bars are to the left in the histograms with a tail of smaller bars to the right as shown in the histograms above.

The distribution of the nongraduates do not appear to contain any outliers, because there are no gaps in the histogram. The distribution of the graduates contains possible outliers, because there are 4 bars in the histogram that are separated from the rest of the bars in the histogram with a gap.

The center of both distributions appears to be roughly between 0 and 10 thousand dollars, as we expect the center to be roughly at the highest bar in the histogram.

The spread of the graduate distributions is greater than the spread for the nongraduate distribution, because the histogram for the graduates is wider compared to the histogram of the nongraduates.