2005 AMC 12B Problems/Problem 9
- The following problem is from both the 2005 AMC 12B #9 and 2005 AMC 10B #19, so both problems redirect to this page.
Contents
Problem
On a certain math exam, of the students got points, got points, got points, got points, and the rest got points. What is the difference between the mean and the median score on this exam?
Solution
To begin, we see that the remaining of the students got points. Assume that there are students; we see that students got points, students got points, students got points, students got points, and students got points. The median is , since the and terms are both . The mean is . The difference between the mean and median, therefore, is .
Solution 2
The remaining of the students got points. The mean is equal to . The score greater than or equal to of other scores is the median. Since scored or lower and the next scored , the median is . The difference between the mean and the median is .
~mobius247
See also
2005 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
2005 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 8 |
Followed by Problem 10 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
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