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Drink H · 2020年01月15日

问一道题:NO.PZ2020010302000007

问题如下:

What are the median and interquartile range? When is the median equal to the mean?

选项:

解释:

The median is the point where 50% of the probability is located on either side. It may not be unique in discrete distributions, although it is common to choose the smallest value where this condition is satisfied.

The IQR is the difference between the 25% and 75% quantiles. These are the points where 25% and 75% of the probability of the random variable lies to the left. This difference is a measure of spread that is like the standard deviation.

The median is equal to the mean in any symmetric distribution if the first moment exists (is finite).

1、“although it is common to choose the smallest value where this condition is satisfied”--这句话怎么理解?

2、“These are the points where 25% and 75% of the probability of the random variable lies to the left”--为什么是在左边?

3、“The median is equal to the mean in any symmetric distribution if the first moment exists (is finite)”--这句话怎么理解?

2 个答案
已采纳答案

品职答疑小助手雍 · 2020年01月15日

1.在离散型分布里,可能找不出中位数使两边都是50%的概率,不过可以通过求最接近的两个数的平均数作为中位数(如果是一个区间可以通过线性插值之类的方法找中位数),总之总能凑出来两边概率相等的那么个数。

2.这第二句话解释的是第一个和第三个四分位点,这两个四分位点分别有25%和75%的参数在他们左边。

3.如果一阶导存在(可以理解为有均值),那么对于对称的分布,均值等于中位数。

梦梦 · 2024年02月29日

老师您好,针对回答的问题1想请教您,假设有四个数,由小到大排列分别为1,2,3,4,那中位数怎么求呢?

品职答疑小助手雍 · 2024年03月01日

(2+3)/2=2.5