2018 AMC 8 第 8 题

先试着解答 2018 AMC 8 第 8 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 2018 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。

8.

Garcia 老师询问健康课的学生上周有多少天至少锻炼了 3030 分钟。结果汇总在下面的条形图中,柱子的高度表示学生人数。
Garcia 老师班上学生报告的上周锻炼天数的平均数是多少?答案四舍五入到最接近的百分之一。
Mr. Garcia asked the members of his health class how many days last week they exercised for at least 3030 minutes. The results are summarized in the following bar graph, where the heights of the bars represent the number of students.
What was the mean number of days of exercise last week, rounded to the nearest hundredth, reported by the students in Mr. Garcia’s class?
3.503.50
3.573.57
4.364.36
4.504.50
5.005.00
答案:C
知识点:平均数数据与图表解读
小提示:
根据条形图高度计算加权平均数
Compute the weighted average from the bar heights.
大提示:
先求学生总数,再求报告的锻炼天数总和
First find the total number of students, then find the total number of reported exercise days.
视频讲解:
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文字解答:
从条形图可知,锻炼 1,2,3,4,5,6,71,2,3,4,5,6,7 天的学生人数依次为 1,3,2,6,8,3,21,3,2,6,8,3,2,学生总数为 2525。
学生报告的锻炼天数总和为 1⋅1+2⋅3+3⋅2+4⋅6+5⋅8+6⋅3+7⋅2=109。\begin{aligned} &1\cdot1+2\cdot3+3\cdot2+4\cdot6\\ &\qquad+5\cdot8+6\cdot3+7\cdot2=109 \end{aligned}\text{。}
平均数为 10925=4.36\frac{109}{25}=4.36 天。
所以正确答案是 C。
The bar heights for 1,2,3,4,5,6,71,2,3,4,5,6,7 days are 1,3,2,6,8,3,21,3,2,6,8,3,2, for a total of 2525 students.
The total number of reported exercise days is 1⋅1+2⋅3+3⋅2+4⋅6+5⋅8+6⋅3+7⋅2=109.\begin{aligned} &1\cdot1+2\cdot3+3\cdot2+4\cdot6\\ &\qquad+5\cdot8+6\cdot3+7\cdot2=109. \end{aligned}
The mean is 10925=4.36\frac{109}{25}=4.36 days.
Thus, C is the correct answer.
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