2014 AMC 12A Problem 5

Problem 5 of 25EasierAlgebra

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 the median of the students’ scores on this quiz?

Show solution

Solution

The remaining

25\%

scored

100.

Since

45\%

scored at most

80

and

75\%

scored at most

90,

the median is

90.

The mean is

\begin{aligned} &0.10(70)+0.35(80)\\ &\quad{}+0.30(90)+0.25(100)\\ &\quad{}=7+28+27+25=87. \end{aligned}

The difference is

90-87=3.

Thus, the correct answer is C.