Home / AP® Exam / AP® Statistics / AP Statistics 1.9 Comparisons of the Distributions for One Quantitative Variable- Exam Style Questions – MCQs

AP Statistics 1.9 Comparisons of the Distributions for One Quantitative Variable- Exam Style Questions - MCQs - New Syllabus

AP Statistics -MCQs and Answers - All Topics

Question 

The stemplot below shows the yearly earnings per share of stock for two different companies over a sixteen-year period.

Which of the following statements is true?

(A) The median of the earnings of Company A is less than the median of the earnings of the Company B.
(B) The range of the earnings of Company A is less than the range of the earnings of Company B.
(C) The third quartile of Company A is smaller than the third quartile of Company B.
(D) The mean of the earnings of Company A is greater than the mean of the earnings of Company B.
(E) The interquartile range of Company A is twice the interquartile range of Company B.

▶️ Answer/Explanation

To compare the two distributions, we can examine their quartiles. Each company has 16 observations, so the third quartile \(Q_3\) is the median of the upper half of the ordered data.

For Company A, the ordered data give:
\( Q_3 = 249 \)
For Company B, the ordered data give:
\( Q_3 = 173 \)
Therefore, Company A’s third quartile is actually larger than Company B’s, so choice (C) is false.
Checking the remaining statements shows that the median of Company A is less than the median of Company B.
Company A median: \( \frac{143+178}{2}=160.5 \)
Company B median: \( \frac{143+153}{2}=148 \)
This shows (A) is not true. Continuing the comparisons, the only statement that is correct is that the mean of Company A exceeds the mean of Company B because Company A contains several much larger values in the upper tail.

✅ Answer: (D)

Question

The manager of an automotive company is interested in comparing the gas mileages for cars manufactured in Country A and cars manufactured in Country B. The manager selected a random sample of \(100\) cars manufactured in Country A and a random sample of \(100\) cars manufactured in Country B. The gas mileages for each sample, in miles per gallon \((\text{mpg})\), are summarized in the boxplots.
Which of the following is the best comparison of the centers and spreads of the two distributions?
(A) Country A has a higher median and a larger interquartile range than Country B.
(B) Country B has a higher median and a larger interquartile range than Country A.
(C) Country A has a higher median, but Country B has a larger interquartile range.
(D) Country B has a higher median, but Country A has a larger interquartile range.
▶️ Answer/Explanation

From the boxplots, the median for Country A is approximately \(18\,\text{mpg}\), while the median for Country B is approximately \(32\,\text{mpg}\). Therefore, Country B has the higher center.

The interquartile range for Country A is approximately \(22-14=8\,\text{mpg}\).
The interquartile range for Country B is approximately \(36-24=12\,\text{mpg}\).

Since \(12\,\text{mpg} > 8\,\text{mpg}\), Country B also has the larger interquartile range.

✅ Answer: (B)

Question

Studies have shown that foods rich in compounds known as flavonoids help lower blood pressure. Researchers conducted a study to investigate whether there was a greater reduction in blood pressure for people who consumed dark chocolate, which contains flavonoids, than for people who consumed white chocolate, which does not contain flavonoids.
Twenty-five healthy adults participated in the study. Of the \(25\) participants, \(13\) were randomly assigned to the dark chocolate group, and the remaining \(12\) were assigned to the white chocolate group. The reduction in blood pressure, in millimeters of mercury \((\text{mmHg})\), was calculated as \(\text{before} – \text{after}\). The reductions are shown in the dotplots.
Which of the following correctly compares the medians of the reductions in blood pressure for the two groups?
(A) The median reduction is \(7\,\text{mmHg}\) for the dark chocolate group and \(0\,\text{mmHg}\) for the white chocolate group; the dark chocolate group has the greater median reduction.
(B) The median reduction is \(0\,\text{mmHg}\) for the dark chocolate group and \(7\,\text{mmHg}\) for the white chocolate group; the white chocolate group has the greater median reduction.
(C) The median reduction is \(6.08\,\text{mmHg}\) for the dark chocolate group and \(0.42\,\text{mmHg}\) for the white chocolate group; the dark chocolate group has the greater median reduction.
(D) The two groups have the same median reduction because the dotplots overlap.
▶️ Answer/Explanation

From the dotplots, the median reduction in blood pressure for the dark chocolate group is \(7\,\text{mmHg}\), and the median reduction for the white chocolate group is \(0\,\text{mmHg}\).
Since \(7>0\), the dark chocolate group has the greater median reduction in blood pressure.
Choice (C) uses the sample means, not the medians. The means are \(\bar{x}_{\text{dark}}=6.08\) and \(\bar{x}_{\text{white}}=0.42\), but the question asks for medians.

✅ Answer: (A)

More AP Statistics MCQ Questions..
Scroll to Top