AMC 8 2013 Problem 5

AMC8 2013 年第 5 题

统计与数据图表★☆☆☆☆
Hammie is in 6th6^\text{th} grade and weighs 106 pounds. His quadruplet sisters are tiny babies and weigh 5, 5, 6, and 8 pounds. Which is greater, the average (mean) weight of these five children or the median weight, and by how many pounds?
Hammie 目前六年级,重 106 磅。她的四胞胎妹妹们现在还是婴儿,分别重 5,5,6,8 磅。 问这 5 个小孩的平均重量和重量的中位数,哪个大?大多少磅?
  1. A.median, by 60\text{median, by 60} / 中位数,大 60
  2. B.median, by 20\text{median, by 20} / 中位数,大 20
  3. C.average, by 5\text{average, by 5} / 平均值,大 5
  4. D.average, by 15\text{average, by 15} / 平均值,大 15
  5. E.average, by 20\text{average, by 20} / 平均值,大 20

正确答案 · Correct Answer

E

解析 · Solution

Solution 1

Listing the elements from least to greatest, we have (5, 5, 6, 8, 106), we see that the median weight is 6 pounds. The average weight of the five kids is 5+5+6+8+1065=1305=26\displaystyle \frac{5+5+6+8+106}{5} = \frac{130}{5} = 26. Hence, 26−6=average, by 20.26-6=\text{average, by 20}.

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