AMC10 2014 A

AMC10 2014 A · Q5

AMC10 2014 A · Q5. It mainly tests Averages (mean), Probability (basic).

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?

在一张代数测验中，10% 的学生得 70 分，35% 得 80 分，30% 得 90 分，其余得 100 分。这张测验学生成绩的平均数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

Because over 50% of the students scored 90 or lower, and over 50% of the students scored 90 or higher, the median score is 90. The mean score is $\frac{10}{100} \cdot 70 + \frac{35}{100} \cdot 80 + \frac{30}{100} \cdot 90 + \frac{25}{100} \cdot 100 = 87$, for a difference of $90 - 87 = 3$.

因为超过 50% 的学生得分 90 分或更低，且超过 50% 的学生得分 90 分或更高，中位数是 90。平均数是 $\frac{10}{100} \cdot 70 + \frac{35}{100} \cdot 80 + \frac{30}{100} \cdot 90 + \frac{25}{100} \cdot 100 = 87$，差值为 $90 - 87 = 3$。

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