2005 AMC 12B Problem 9

Question

On a certain math exam,

10\%

of the students got

70

points,

25\%

got

80

points,

20\%

got

85

points,

15\%

got

90

points, and the rest got

95

points. What is the difference between the mean and the median score on this exam?

0

1

2

4

5

The remaining percentage scored

95

:

100 - 10 - 25 - 20 - 15

For the median, find where the cumulative percentage passes

50\%

The percentage scoring

95

is

100 - 10 - 25 - 20 - 15 = 30.

The mean is

\begin{aligned} &0.10(70) + 0.25(80) \\ &\quad {}+ 0.20(85) + 0.15(90) \\ &\quad {}+ 0.30(95) = 86. \end{aligned}

Cumulatively,

10\%

are below

80,

35\%

are at or below

80,

and

55\%

are at or below

85.

The middle scores fall at

85,

so the median is

85.

The difference is

86 - 85 = 1.

Thus, the correct answer is B.

Problem 9 in other years