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List L:4, 5, 6, 7, 7, 8, xList L consists of 7 numbers. Which of the following
List L:4, 5, 6, 7, 7, 8, xList L consists of 7 numbers. Which of the following
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2025-02-23
9
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问题
List L:4, 5, 6, 7, 7, 8, x
List L consists of 7 numbers. Which of the following sets consists of all values of x for which the average (arithmetic mean) of the numbers in L is less than the median of the numbers in L?
选项
A、The values of x such that x<5
B、The values of x such that 37/6<x<12
C、The values of x such that x<5 or 37/6<x<12
D、The values of x such that 5<x<37/6
E、The values of x such that 5<x<37/6 or x>12
答案
C
解析
本题可使用两种解题方法。
(1)方法一,分类讨论。
①x大于中位数时,此时中位数为(37+x)/7<7,得x<12。
②x等于中位数时,此时中位数为(37+x)/7<x,得x>37/6。
③x小于中位数时,此时中位数为6,则(37+x)/7<6,得x<5。
(2)方法二,观察选项。发现所给的范围的临界值是5,37/6,12,则只需判断x取这几个值之间的数是否符合平均值小于中位数即可。故答案为C。
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