2014 AMC 12A Problem 5

Attempt Problem 5 of the 2014 AMC 12A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2014 AMC 12A solutions, or check the answer key.

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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?

1

2

3

4

5

The median is the score of the middle student after ordering everyone

Compute the weighted mean

0.10(70)+0.35(80)

+0.30(90)+0.25(100)

and compare it to the median

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.

Problem 5 in other years