1994 AMC 12 第 24 题
先试着解答 1994 AMC 12 第 24 题，然后核对你的答案与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 1994 AMC 12 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
24.
一个由五个观测值组成的样本，算术平均数为 ，中位数为 。这样的样本可能达到的极差（最大观测值减最小观测值）的最小值是
A sample consisting of five observations has an arithmetic mean of and a median of The smallest value that the range (largest observation minus smallest) can assume for such a sample is
答案：C
小提示：
将观测值依次排列为
Order the observations as
大提示：
利用总和 ，再检验能否使极差小于
Use the total sum , then test whether a range below is possible
解答：
样本 的总和为 ，中位数为 ，极差为 ，所以极差 可以达到。假设极差至多为 。若最大值至多为 ，则最大的三个值都必须是 ，余下两个较小值之和为 ；但它们都至少为 ，产生矛盾。若最大值大于 ，则最小值大于 ，使总和大于 。因此更小的极差不可能达到。正确答案是 C。
The sample has sum median and range so range is possible. Suppose the range were at most If the largest value were at most then the top three values would all be leaving the bottom two with sum yet each would be at least a contradiction. If the largest value exceeded then the smallest would exceed making the total exceed Thus no smaller range works. The correct answer is C.
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