A certain list of 200 test scores has an average (arithmetic mean) of 85 and a standard deviation of d, where d is positive

题目

A certain list of 200 test scores has an average (arithmetic mean) of 85 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 202 test scores with a standard deviation less than d ?

选项

80 and 80

80 and 85

80 and 90

85 and 85

85 and 90

解析

集合的标准差体现了数据与均值的偏离程度，即数据的分散程度：标准差小意味着数据点接近均值，标准差大则说明数据在较大范围内分散。因此，当添加远离均值的数时，集合会被“拉开”，标准差变大；当添加接近均值的数时，集合会被“收缩”，标准差变小。根据上述结论，添加**最接近均值的两个数**会让集合收缩得最明显，从而使标准差的减小幅度最大。最接近均值的数是85和85（实际上它们等于均值），添加这两个数必然会收缩集合，进而让标准差减小得最多。答案：D

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