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2014 AMC 10A Problem 5

Problem 5 of 25EasierAlgebra

On an algebra quiz, 10%10\% of the students scored 7070 points, 35%35\% scored 8080 points, 30%30\% scored 9090 points, and the rest scored 100100 points. What is the difference between the mean and the median of the students’ scores on this quiz?

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Solution

The median is 9090, because 45%45\% of the students scored below 9090 and 25%25\% scored above 9090. The mean is 0.10⋅700.10\cdot70 +0.35⋅80+0.35\cdot80 +0.30⋅90+0.30\cdot90 +0.25⋅100=87+0.25\cdot100=87. The difference is 90−87=390-87=3. Thus, C is the correct answer.

More practice

Concepts: mean · median (data)

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.