2. 外语
  3. 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 a

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 a

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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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