2014 AMC 10A Problem 5

Below is the professionally curated solution for Problem 5 of the 2014 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2014 AMC 10A solutions, or check the answer key.

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Concepts:mean median (data)

Difficulty rating: 1280

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 median score of the students' scores on this quiz?

$1$

$2$

$3$

$4$

$5$

Solution:

The median is $90$ , because $45\%$ of the students scored below $90$ and $25\%$ scored above $90$ .

The mean is $0.10\cdot70+0.35\cdot80+0.30\cdot90+0.25\cdot100=87$ .

The difference is $90-87=3$ .

Thus, C is the correct answer.

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