关于均数和中位数，说法正确吗？

统计问题（28）：关于均数和中位数，说法正确吗？

一家医院里患者中风后的平均住院时间为21天，中位数为12天，标准差为13天。那么对于这些信息，下面说法哪些是正确的？(多选)

Question

The mean length of stay in one hospital after stroke was 21days, the median was 12 days, and the standard deviation was 13 days. Which ofthe following, if any, are true?

a) The typical length of stay was 21 days

b) The mean length of stay may be affected by long stay patients

c) As many patients stayed for fewer than 12 days as stayed longer than 12 days

d) When comparing length of stay in this hospital with that in another hospital, survival methods would be preferable to a t test

Answer

The typical value is hard to define. It might be the most frequent length of stay, which would be the mode. But if there are a large number of values then the mode may be true for only a few people. The median value is sometimes used because it is in the middle of the rank order. In a skewed distribution such as this, the mean is a lot higher than the median, because of long stay patients, and few people may stay for close on 21 days. The mean is certainly not the typical value here.

Answer c is one way of defining the median.

Survival methods are ideallysuited to measuring “time to event.” The event in this case would be dischargefrom hospital. These methods do not require a near normal distribution ofvalues as is preferable when using a t test.

中文解释：

从这个数据中很难确定典型值，一般典型值可能是频数最多住院时间，也就是众数。但是，大样本情况下，则众数也值代表着少数人。有时使用中位数作为典型值值，因为它处于住院天数顺序的中间。在这样的偏斜分布中，由于患者长期住院，其平均值比中位数高很多，很少有人可以在21天之内住院。平均值当然不是此处的典型值。

答案c是定义中位数的一种方法。

生存分析方法非常适合测量“事件发生时间”。在这种情况下，该事件定义为“出院”。生存分析法不需要t检验那样要求数据近似正态分布。

所以答案是选择 B,C,D

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