1996 AMC 12 第 4 题

Question

一个由九个整数组成的数列中，有六个数是

7

、

8

、

3

、

5

、

9

和

5

。这九个数的中位数可能达到的最大值是

Six numbers from a list of nine integers are

7,

8,

3,

5,

9,

and

5.

The largest possible value of the median of all nine numbers in this list is

5

6

7

8

9

将九个数排序后，中位数是第五个数

The median is the fifth number after all nine are sorted

要使中位数最大，可以把三个未给出的数都取到足够大

To maximize the median, take each of the three unspecified numbers as large as needed

六个已知数按顺序排列为

3,5,5,7,8,9

。即使三个未给出的整数都大于

9

，完整数列中的第五个数仍为

8

。这个值可以达到，所以正确答案是 D。

The six specified values in order are

3,5,5,7,8,9.

Even if all three unspecified integers exceed

9,

the fifth entry of the full sorted list is

8.

This is attainable, so the correct answer is D.

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