AMC10 2005 B

AMC10 2005 B · Q19

AMC10 2005 B · Q19. It mainly tests Averages (mean).

On a certain math exam, 10% of the students got 70 points, 25% got 80 points, 20% got 85 points, 15% got 90 points, and the rest got 95 points. What is the difference between the mean and the median score on this exam?

在某次数学考试中，10% 的学生得 70 分，25% 得 80 分，20% 得 85 分，15% 得 90 分，其余得 95 分。这次考试的平均分与中位数的差是多少？

(A) 0 0

(B) 1 1

(D) 4 4

(E) 5 5

Answer

Correct choice: (B)

正确答案：（B）

Solution

(B) The percentage of students getting 95 points is $100-10-25-20-15=30$, so the mean score on the exam is $0.10(70)+0.25(80)+0.20(85)+0.15(90)+0.30(95)=86.$ Since fewer than half of the scores were less than 85, and fewer than half of the scores were greater than 85, the median score is 85. The difference between the mean and the median score on this exam is $86-85=1$.

（B）得到95分的学生所占百分比为 $100-10-25-20-15=30$，因此本次考试的平均分为 $0.10(70)+0.25(80)+0.20(85)+0.15(90)+0.30(95)=86.$ 由于低于85分的成绩不到一半，高于85分的成绩也不到一半，所以中位数为85。本次考试平均数与中位数之差为 $86-85=1$。

Topics

AR.006 Averages (mean)