2014 AMC 10A Problems/Problem 5

Problem

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?

$\textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}}\ 4\qquad\textbf{(E)}\ 5$ (Error compiling LaTeX. Unknown error_msg)

Solution

WLOG let there be $100$ students who took the test. We have $10$ students score $70$ points, $35$ students score $80$ points, $30$ students score $90$ points and $25$ students score $100$ points. The median is easy to find by simply eliminating members from each group. The median is $90$ points. The mean is just $\dfrac{700+2800+2700+2500}{100}=7+28+27+25=87$ . The difference is $90-87=\boxed{\textbf{(C)}\ 3}$

2014 AMC 10A (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
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2014 AMC 10A Problems/Problem 5

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