Question

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?

$1$

$2$

$3$

$4$

$5$

Answer: C

Concepts:mean median (data)percentage

Difficulty rating: 1270

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 $\begin{aligned} &0.10(70)+0.35(80)\\ &\quad{}+0.30(90)+0.25(100)\\ &\quad{}=7+28+27+25=87. \end{aligned}$

The difference is $90-87=3.$

Thus, the correct answer is C.

2014 AMC 12A Problem 5

Answer: C

Difficulty rating: 1270

Solution:

Problem 5 in Other Years