Problem-Solving and Data AnalysisVery hardMean from a frequency distribution
Problem-Solving and Data Analysis practice question
On a test, 3 students scored 70, 5 students scored 80 and 2 students scored 100. What is the mean score of the 10 students?
Answer: 81
The mean needs the total of all ten scores: 3(70) + 5(80) + 2(100) = 210 + 400 + 200 = 810. Divide by 10 students: 81.
Common wrong answers
- If you answered 80
- 80 is the most common score, the mode. The mean weights every score by how many students got it: 810 / 10.
- If you answered 250
- 250 is 70 + 80 + 100, the three distinct scores added. Each must be multiplied by its number of students first.
- If you answered 83.3
- 83.3 is (70 + 80 + 100) / 3 — averaging the three distinct scores as if one student got each. Five students scored 80, which pulls the mean down.
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