题目

Set Y contains elements {2, 4, 6, 8} which of the following sets have smaller standard deviation than set Y?

I. {22, 24, 26, 28}
II. {-4, -2, -8, -6, -10}
III. {0, 2, 4, 6}

选项

A.

I only

B.

II only

C.

III only

D.

I and III

E.

None of above

解析

已知集合\(Y = \{2, 4, 6, 8\}\) \(Y\)的均值 = \(\frac{4 + 6}{2} = 5\) 各项与均值的偏差 = \(\{2-5, 4-5, 6-5, 8-5\}\) = \(\{-3, -1, 1, 3\}\) ### I. \(\{22, 24, 26, 28\}\) 均值 = \(\frac{24 + 26}{2} = 25\) 各项与均值的偏差 = \(\{22-25, 24-25, 26-25, 28-25\}\) = \(\{-3, -1, 1, 3\}\) 因此,**标准差与\(Y\)相同** ### II. \(\{-4, -2, -8, -6, -10\}\) 按升序排列:\(\{-10, -8, -6, -4, -2\}\) 均值 = \(-6\) 各项与均值的偏差 = \(\{-4, -2, 0, 2, 4\}\) 因此,**标准差大于\(Y\)** ### III. \(\{0, 2, 4, 6\}\) 均值 = \(\frac{2 + 4}{2} = 3\) 各项与均值的偏差 = \(\{0-3, 2-3, 4-3, 6-3\}\) = \(\{-3, -1, 1, 3\}\) 因此,**标准差与\(Y\)相同** 答案:选项E
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