2010 AMC 8 第 4 题

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所有题目均经美国数学协会(MAA)官方合法授权使用。

4.

2,3,0,3,1,4,0,32,3,0,3,1,4,0,3 的平均数、中位数和众数之和是多少?

What is the sum of the mean, median, and mode of the numbers 2,3,0,3,1,4,0,3?2,3,0,3,1,4,0,3?

 6.5\ 6.5

 7\ 7

 7.5\ 7.5

 8.5\ 8.5

 9\ 9

答案:C
知识点:平均数中位数(数据)众数
难度评级:720
解答:

重新排序后的列表是 0,0,1,2,3,3,3,40,0,1,2,3,3,3,4

中位数是中间两个数的平均数,即 2+32=2.5\dfrac{2+3}2 = 2.5。众数是 33,因为 33 出现次数最多。平均数为 0+0+1+2+3+3+3+48 \dfrac{0+0+1+2+3+3+3+4}{8} =168=2. = \dfrac{16}{8} = 2 .

它们的和为 2.5+3+2=7.52.5+3+2 = 7.5

所以正确答案是 C

The list reordered is 0,0,1,2,3,3,3,4.0,0,1,2,3,3,3,4.

The median is the mean of the middle two numbers, which would be 2+32=2.5.\dfrac{2+3}2 = 2.5. The mode is 33 since 33 appears the most. The mean is 0+0+1+2+3+3+3+48 \dfrac{0+0+1+2+3+3+3+4}{8}=168=2. = \dfrac{16}{8} = 2 .

Their sum is 2.5+3+2=7.5.2.5+3+2 = 7.5.

Thus, the answer is C .

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