2013 AMC 8 第 5 题

先试着解答 2013 AMC 8 第 5 题,然后核对你的答案与视频与精心整理的解答,解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2013 AMC 8 解答,或核对答案。

所有题目均经美国数学协会(MAA)官方合法授权使用。

5.

汉米上 66 年级,体重 106106 磅。他的四胞胎妹妹还是小婴儿,体重分别为 55、55、66 和 88 磅。这五个孩子的平均体重和中位数哪个更大,大多少磅?
Hammie is in the 66th grade and weighs 106106 pounds. His quadruplet sisters are tiny babies and weigh 5,5, 5,5, 6,6, and 88 pounds. Which is greater, the average (mean) weight of these five children or the median weight, and by how many pounds?
中位数,大 6060 磅
median, by 6060
中位数,大 2020 磅
median, by 2020
平均数,大 55 磅
average, by 55
平均数,大 1515 磅
average, by 1515
平均数,大 2020 磅
average, by 2020
答案:E
知识点:平均数中位数(数据)
小提示:
先把五个体重排序,再找中位数
Order the five weights before finding the median.
大提示:
将中位数与总体重除以 55 比较
Compare the median with the total weight divided by 55.
视频讲解:
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文字解答:
体重的中位数就是排序后正中间的那个值,可以这样找出: 5,5,6‾,8,106 \cancel{ 5 },\cancel{ 5 },\underline{6},\cancel{8},\cancel{106} 因此中位数是 66 磅。
平均数可以计算如下: 106+5+5+6+85=1305=26。 \begin{align*} &\dfrac{106 + 5 + 5 + 6 + 8}{5} \\&= \dfrac{130}{5}\\ &= 26\text{。} \end{align*} 这个值比中位数大,具体来说,平均数比中位数大 2020 磅。
所以正确答案是 E。
The median weight is the middle value, which we can find as: 5,5,6‾,8,106\cancel{ 5 },\cancel{ 5 },\underline{6},\cancel{8},\cancel{106} Therefore, the median is 66 pounds.
The average (mean) can be calculated to be: 106+5+5+6+85=1305=26. \begin{align*} &\dfrac{106 + 5 + 5 + 6 + 8}{5} \\&= \dfrac{130}{5}\\ &= 26. \end{align*} This is greater than the median, specifically, the mean is 2020 pounds greater than the median.
Thus, E is the correct answer.
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