Question

一次代数小测中， $10\%$ 的学生得 $70$ 分， $35\%$ 得 $80$ 分， $30\%$ 得 $90$ 分，其余得 $100$ 分。本次小测成绩的平均数与中位数之差是多少？

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?

$1$

$2$

$3$

$4$

$5$

答案：C

知识点：平均数中位数（数据）百分数

难度评级：1270

解答：

其余 $25\%$ 的学生得 $100$ 分。由于 $45\%$ 的学生得分不超过 $80$ ，而 $75\%$ 的学生得分不超过 $90$ ，所以中位数是 $90$ 。

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

两者之差为 $90-87=3$ 。

所以正确答案是 C。

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 第 5 题

答案：C

难度评级：1270

解答：

其他年份的第 5 题