Digital PSAT Math Practice Question 232: Answer and Explanation

Question: 232

In the above histogram, the distribution of the number of hours of sleep per night as self-reported by thirty 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 you can't sum together all of the responses without knowing the actual numerical responses (you only know 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 them from smallest to largest, 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 will be between 6 and 7 hours. Thus, the median and mode are the same, answer (C).