PSAT Math Multiple-Choice Question 791: Answer and Explanation

Question: 791

In the below histogram, the distribution of the number of hours of sleep per night as self-reported by 30 students is recorded. Which of the following values would be equal for the above set of values?

• A. Mean and median
• B. Mode and mean
• C. Median and mode
• D. Mean and range

Correct Answer: C

Explanation:

(C) In this problem, the mean can't easily be figured out because we can't sum together all of the responses without knowing the actual numerical responses. (We know only the range of hours for each student.) The mode is between 6 and 7 hours since this was the most frequent response (12 students chose this range). The median in a series of 30 terms is found by arranging the terms from smallest to largest and then taking the average of the 15th and 16th terms. In this case, the 15th and 16th terms are both between 6 and 7 hours, so the median is between 6 and 7 hours. Thus, the median and mode are the same, which is choice (C).