Problem-Solving and Data AnalysisVery hardGroup size from a combined mean
Problem-Solving and Data Analysis practice question
A class of 24 students has a mean test score of 70. A second class has a mean score of 82. When the two classes are combined, the mean score is 74. How many students are in the second class?
Answer: 12
Let n be the second class's size. Total points: 24(70) + 82n = 74(24 + n). So 1,680 + 82n = 1,776 + 74n, giving 8n = 96 and n = 12.
Common wrong answers
- If you answered 8
- 8 is the coefficient after collecting terms (8n = 96), not n itself.
- If you answered 24
- 24 assumes the classes are the same size, but then the combined mean would be 76, not 74.
- If you answered 96
- 96 is the right side after collecting terms; divide by 8.
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