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大瓶子 · 2023年08月20日

The arithmetic sum of the deviations around the mean是什么意思 ?

NO.PZ2022123001000028

问题如下:

The least accurate statement about measures of dispersion for a distribution is that the:

选项:

A.range provides no information about the shape of the data distribution B.arithmetic average of the deviations around the mean will be equal to one C.mean absolute deviation will be either less than or equal to the standard deviation

解释:

B is correct. The arithmetic sum of the deviations around the mean will always equal zero, not one.

A is incorrect. Range does not provide information about the shape of the distribution.

C is incorrect. The mean absolute deviation will always be less than or equal to the standard deviation.

B选项是什么意思,计算过程是怎么样的?

1 个答案

星星_品职助教 · 2023年08月20日

“deviation around the mean”为对均值X bar做差,即对于分布中的任意一个 Xi,deviation around the mean就是 Xi-X bar。

由于X bar=(X1+X2+...+Xi)/n,可得X1+X2+...+Xi=nX bar。

所以,所有Xi - X bar的和 = (X1- X bar)+ (X2- X bar)+...+ (Xi- X bar)=X1+X2+...+Xi - nX bar =0.