Question

Value of a diploma Do students who graduate from high school earn more money than students who do not? To find out, we took 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.

Part (a). Would it be appropriate to use frequency histograms instead of relative frequency histograms in this setting? Explain why or why not.

Part (b). Compare the distributions of total personal income for the two groups.

Short answer

Part (a) No

Part (b)

Both distributions lean to the right.

The distribution of nongraduates appears to be devoid of outliers, whereas the distribution of graduates may contain outliers.

The center of both distributions appears to be somewhere between 0 and $10,000.

The spread of graduate distributions is larger than the spread of nongraduate distributions.

Step-by-step solution

Part (a) Step 1 Given information. 

Each person's educational level and total personal income were recorded. The relative frequency histograms show the data for the 57 non-graduates (No) and the 314 graduates (Yes).

Part (a) Step 2  In this case, would frequency histograms be preferable to relative frequency histograms

No, because the two histograms do not use the same number of data values, it would not be appropriate to use frequency histograms instead of relative frequency histograms (as there are 314 graduates but only 57 non graduates). Because these two histograms are not based on the same number of data values, we cannot compare the frequency histograms.

As a result:

No

Part (b) Step 1 The distributions of total personal income for the two groups. 

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

Because there are no gaps in the histogram, the distribution of nongraduates does not appear to contain any outliers. Because there are four bars in the histogram that are separated from the rest of the bars in the histogram by a gap, the distribution of graduates contains potential outliers.

The center of both distributions appears to be between 0 and 10,000 dollars, as we would expect it to be at the highest bar in the histogram.

Because the histogram for graduates is wider than the histogram for nongraduates, the spread for graduate distributions is greater than the spread for nongraduate distributions.

As a result:

Both distributions lean to the right.

The distribution of nongraduates appears to be devoid of outliers, whereas the distribution of graduates may contain outliers.

The center of both distributions appears to be somewhere between 0 and $10,000.

The spread of graduate distributions is larger than the spread of nongraduate distributions.