AMC12 2014 A

AMC12 2014 A · Q5

AMC12 2014 A · Q5. It mainly tests Averages (mean), Casework.

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?

在一张代数测验中，$10\%$的学生得分$70$分，$35\%$得分$80$分，$30\%$得分$90$分，其余得分$100$分。学生成绩的平均分与中位数的差是多少？

(A) 1 1

(B) 2 2

(D) 4 4

(E) 5 5

Answer

Correct choice: (C)

正确答案：（C）

Solution

WLOG, let there be $20$ students (the least whole number possible) who took the test. We have $2$ students score $70$ points, $7$ students score $80$ points, $6$ students score $90$ points and $5$ students score $100$ points. Therefore, the mean is $87$ and the median is $90$. Thus, the solution is \[90-87=3\implies\boxed{\textbf{(C)} \ 3}\]

不妨设有$20$名学生（最小整数）。则$2$人$70$分，$7$人$80$分，$6$人$90$分，$5$人$100$分。因此平均分是$87$，中位数是$90$。于是，$90-87=3\implies\boxed{\textbf{(C)} \ 3}$

Topics