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Luyiling · 2021年08月05日

positively skewed distribution的mean

NO.PZ2017092702000159

问题如下:

Which of the following sequences best represents the relative sizes of the mean, median, and mode for a positively skewed unimodal distribution?

选项:

A.

mode ≤ median ≤ mean

B.

mode < median < mean

C.

mean < median < mode

解释:

B is correct. For the positively skewed unimodal distribution, the mode is less than the median, which is less than the mean.
A is incorrect because, for the positively skewed unimodal distribution, the mode is less than the median (not less than or equal to), which is less than (not less than or equal to) the mean.
C is incorrect because, for the negatively (not positively) skewed unimodal distribution, the mean is less than the median, which is less than the mode.


麻烦老师讲一下positively skewed distribution的mean为什么大于media,突然钻牛角尖绕进去了

1 个答案

星星_品职助教 · 2021年08月05日

同学你好,

positive/right skewed意味着在右侧有一条长尾。这代表在右侧出现了很大的极端值。

这些大的极端值就会把均值整体都往右边拉。但中位数受极端值的影响相较小。

例如有11个数字,最大的数字无论是100还是1亿都不影响中位数是第6个数,但后者会把均值提升很多。

所以右侧极端值(positive/right skewed)会导致mean被拉到右边,从而大于median。