Class students average 15.8 years, with boys averaging 16.4 years and girls 15.4 years. What is the boy-to-girl ratio in the class___________?
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Answer: B. 2:3
Explanation
The alligation method calculates the weighted average ratio by finding the differences between subgroup means and the overall mean. The difference between the girls' average and the overall class average equals sixteen point eight minus fifteen point four equals zero point four. The difference between the overall average and the boys' average equals sixteen point four minus fifteen point eight equals zero point six, giving a ratio of zero point four to zero point six, or two to three. Alligation is a standard mathematical rule used to solve mixture problems involving weighted averages of two groups. The overall average of a combined group always lies mathematically between the averages of its individual subgroups. Ratio simplification reduces decimal proportions into the smallest possible whole number integer representations.
Option A suggests an incorrect ratio that fails to satisfy the alligation difference calculation. Option C reverses or miscalculates the subgroup distance intervals from the overall mean. Option D produces a proportion that violates the weighted average balance required by the class data.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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