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? \textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}}\ 4\qquad\textbf{(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 number present at the 50% mark, which is 90. 90-87 equals 3, which is \textbf{(C)}\ 3\qquad .