AMC 8 2012 Problem 22

AMC8 2012 年第 22 题

统计与数据图表★★★☆☆

Let

R

be a set of nine distinct integers. Six of the elements are 2 , 3 , 4 , 6 , 9 , and 14 . What is the number of possible values of the median of

R

R 是由 9 个不同的整数组成的集合。其中 6 个元素是 2,3,4,6,9 和 14．那么 R 的中位数有多少个可能的值？

A. $\hspace{.05in}4$
B. $\hspace{.05in}5$
C. $\hspace{.05in}6$
D. $\hspace{.05in}7$
E. $\hspace{.05in}8$

正确答案 · Correct Answer

解析 · Solution

Solution 1

Let the values of the missing integers be x, y, z. We will find the bound of the possible medians. The smallest possible median will happen when we order the set as

\{x, y, z, 2, 3, 4, 6, 9, 14\}

. The median is 3. The largest possible median will happen when we order the set as

\{2, 3, 4, 6, 9, 14, x, y, z\}

. The median is 9. Therefore, the median must be between 3 and 9 inclusive, yielding 7 possible medians.

继续练习

免费刷 2012 整卷 →