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The least and greatest number in a list of 7 real numbers are 2 and 20, respectively. The median of the list is 6, and the numbe
The least and greatest number in a list of 7 real numbers are 2 and 20, respectively. The median of the list is 6, and the numbe
admin
2019-05-11
52
问题
The least and greatest number in a list of 7 real numbers are 2 and 20, respectively. The median of the list is 6, and the number 3 occurs most often in the list. Which of the following could be the average of the numbers in the list? Indicate all such numbers.
选项
A、7
B、8.5
C、10.5
答案
A,B,C
解析
若将7个数字从小到大排列,则按照目前的信息可以确定如下数字:
现在只有第五和第六两个数字无法确定,这组数列的平均数的取值范围取决于这两个数的取值。思考它们的最大值和最小值。最大的情况是第五和第六位数字无限趋近于20(不能等于20,否则与3出现次数最多矛盾),此时计算出的平均值为10.57。最小的情况是第五和第六位数字无限趋近于6(不能等于6,否则与3出现次数最多矛盾),此时计算出的平均值为6.57。则平均值可以是6.57-10.57之间的任意数字,ABC选项均正确。本题仅说数列中的数字为“number”实数,没有说是“integer”整数,因此不能看已经给出的其他数字均为整数就默认第五个和第六个数字也为整数。在做题之前,务必看清变量的取值范围。
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