PSAT Math Multiple-Choice Question 640: Answer and Explanation

Question: 640

The high school principal wants to evaluate the effectiveness of the teachers in getting their students to complete the summer reading assignments. The principal assigns 5 points to each student who completes the assignment and gives 0 points to each student who fails to complete the assignment. What is the difference between the mean and the median of the point values given to students in Mr. Walker's class?

• A. 1.38
• B. 1.60
• C. 2.26
• D. 2.74

Correct Answer: C

Explanation:

(C) In Mr. Walker's class, 14 students completed summer reading and earned 5 points, accounting for 14(5) = 70 points. The remaining 17 students received 0 points. So the total points for the class were 70. There are 31 students in the class, so the mean is:

70 ÷ 31 = 2.26

To find the median, list the students' point values from smallest to largest. There are 17 students who earned 0 followed by 14 students who each earned 5. The median term in a 31-term series is the 16th term. (There are 15 terms on the left of the 16th term and 15 terms on the right of the 16th term.) The 16th value is 0, so the median is 0. The difference between the mean and the median, therefore, is:

2.26 - 0 = 2.26

Choice (C) is correct.