2014 AMC 12A Problems/Problem 5

Problem 5

On an algebra quiz, 10% of the students scored 70 points, 35% scored 80 points, 30% scored 90 points, and the rest scored 100 points. What is the difference between the mean and median score of the students' scores on this quiz?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

Solution

The mean can solved by the following. 10% of 70 is 7, 35% of 80 is 28, 30% of 90 is 27, and (100% - 10% - 35% - 30%) = 25%. 25% of 100 is 25. 7 + 28 + 27 + 25 = 87.
The median can be solved by finding the score present at the 50% mark, which is 90.
90-87 equals 3, which is (C) 3.