2005 AMC 10B Problem 19

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;

find it first

For the median, find which score the middle student earned using the cumulative percentages

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}

Since

35\%

scored below

85

and

35\%

scored above

85,

the middle student scored

85,

so the median is

85.

The difference is

86 - 85 = 1.

Thus, B is the correct answer.

Problem 19 in other years