2018 AMC 8 Problem 8

Attempt Problem 8 of the 2018 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2018 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

8.

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?
3.50 3.50
3.57 3.57
4.36 4.36
4.50 4.50
5.00 5.00
Answer: C
Concepts:meandata and graph interpretation
Small hint:
Compute the weighted average from the bar heights.
Big hint:
First find the total number of students, then find the total number of reported exercise days.
Video solution:
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Written solution:
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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