作者chliao2006 (chien)
看板Statistics
标题[问题] variance=0，sample mean=sample median?
时间Wed Apr 22 12:19:36 2015
这是1997年AP Statistics测验里的一个问题：
A random sample of size 10 was taken from a population.
The sample has a variance of zero.
Which of the following statements must be true?
1.The population also has a variance of zero.
2.The sample mean is equal to the sample median.
3.The ten data points in the sample are equal in numerical value.
(a) 1 only
(b) 2 only
(c) 3 only
(d) 1 and 2
(e) 2 and 3
答案是：(c)
但是不理解，为何答案不是(e)？
∵The sample has a variance of zero.
∴The ten data points in the sample are equal in numerical value.
那麽不是同时也可得出，The sample mean is equal to the sample median.
请问为何上面这句不正确？
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1F：推 allen1985: 答案错了？ 04/22 12:50
2F：推 expiate: 你查一下median在偶数时该怎麽算应该就会理解了 04/22 13:09
3F：→ expiate: 我好像理解错了，请忽略我上面的推文，抱歉 04/22 13:13
4F：推 ww770829: 他应该是认为不存在中位数? 04/22 13:30
5F：→ celestialgod: 我也觉得他应该认为没有中位数，全部一样 04/22 13:34
6F：推 allen1985: Median always exists? 04/22 15:18
7F：→ BugEater: 我选e 04/22 16:04
9F：→ celestialgod: 所以是E 04/22 17:04
10F：推 goshfju: 原po是对的 04/23 00:11
11F：推 goshfju: 1. 显然是错的 随便找都有反例 04/23 00:13
12F：推 goshfju: 样本变异数0就代表样本10个数字都ㄧ样（3对）而样本平均 04/23 00:15
13F：→ goshfju: 数跟样本中位数也是那个数字（2对） 04/23 00:15
14F：→ chliao2006: 多谢大家的回答，帮助考量到关於存在的问题。 04/23 02:18