AMC 8 2019 Problem 10
AMC8 2019 年第 10 题
统计与数据图表★★☆☆☆
The diagram shows the number of students at soccer practice each weekday during last week. After computing the mean and median values, Coach discovers that there were actually 21 participants on Wednesday. Which of the following statements describes the change in the mean and median after the correction is made?
下面这张图展示了上周的每个工作日某个足球训练场的学生数。在计算完平均值和中位数之后，教练发现周三实际有 21 个参加者。那么当纠正了这个错误后，下面对于平均数和中位数的改变的论断中，哪个是正确的？
- A.The mean increases by 1 and the median does not change / 平均值增加 1，中位数不变
- B.The mean increases by 1 and the median increases by 1 / 平均值增加 1，中位数增加 1
- C.The mean increases by 1 and the median increases by 5 / 平均值增加 1，中位数增加 5
- D.The mean increases by 5 and the median increases by 1 / 平均值增加 5，中位数增加 1
- E.The mean increases by 5 and the median increases by 5 / 平均值增加 5，中位数增加 5
正确答案 · Correct Answer
B
解析 · Solution
Solution 1
On Monday, 20 people come. On Tuesday, 26 people come. On Wednesday, 16 people come. On Thursday, 22 people come. Finally, on Friday, 16 people come. 20+26+16+22+16=100, so the mean is 20. The median of (16, 16, 20, 22, 26) is 20. The coach figures out that actually 21 people come on Wednesday. The new mean is 21, while the new median of (16, 20, 21, 22, 26) is 21. Also, the median increases by 1 because now the median is 21 instead of 20. The median and mean both change, so the answer is. Another way to compute the change in mean is to notice that the sum increased by 5 with the correction. So, the average increased by 5/5 = 1. Then, the median is computed the same way.
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