2014 AMC 12A 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 the median of the students’ scores on this quiz?

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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.

Tagged: mean · median (data) · percentage