2005 AMC 12B Problem 9

Below is the professionally curated solution for Problem 9 of the 2005 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2005 AMC 12B solutions, or check the answer key.

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Concepts:mean median (data)

Difficulty rating: 1410

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?

$0$

$1$

$2$

$4$

$5$

Solution:

The percentage scoring $95$ is $100 - 10 - 25 - 20 - 15 = 30.$

The mean is $0.10(70) + 0.25(80) + 0.20(85) + 0.15(90) + 0.30(95) = 86.$

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.

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