2014 AMC 12A Problem 5

Below is the professionally curated solution for Problem 5 of the 2014 AMC 12A, 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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Concepts:mean median (data)percentage

Difficulty rating: 1270

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?

$1$

$2$

$3$

$4$

$5$

Solution:

The remaining $25\%$ scored $100.$ Since $45\%$ scored at most $80$ and $75\%$ scored at most $90,$ the median is $90.$

The mean is $0.10(70)+0.35(80)+0.30(90)+0.25(100)=7+28+27+25=87.$

The difference is $90-87=3.$

Thus, the correct answer is C.

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