两道ＰＲＥＰ的ＰＳand DS题

Last month 15 homes were sold in Town X. The average (MA) sale price of the homes was 150,000. And the median sale price was 130,000. which of the following statements must be true?

I. at least one of the homes was sold for more than 165,000

II at least one of the homes was sold for more than 130,000 and less than 150,000

II at least one of the homes was sold for less than 130,000

A. I only   B. II only   C. III only   D. I & II    E. I & III

答案是Ａ．不明白为什么ＩＩＩ不正确．看了一些讨论，有的认为有可能八个卖价最低的都卖了130,000.但问题是如果这样一来怎么能让Median维持在130,000?

Is Z equal to the median of the three positive integers X, Y and Z?

1.> X < Y+Z

2.> Y=Z

答案是Ｂ，我的问题是既然Ｙ＝Ｚ，　那么这三个数的Median应该是Ｘ与Ｙ的算数平均数．是不是我对Median的理解有误？

Median是奇数个数中数值最中间的那个，是偶数个数最中间的两个数的算数平均数．

上面红字是我个人的理解，不对的还请各位指正，尤其第一题，也想听听讲解。

关于median，OG上基本概念部分是这样讲解的，LZ可以看看：

For the data 6,4,7,10,4, the numbers, in order, are 4,4,6,7,10, and the median is 6, the middle number.

For the numbers 4,6,6,8,9,12, the median is (6+8)/2=7. Note the mean of these numbers is 7.5.