Weighted class average: A class has 15 boys and 10 girls with an overall average weight of 38.4 kg. If the boys average 40 kg, find the average weight of the girls.
Correct Answer: 36 kg
Introduction / Context:The task is a direct application of weighted averages. Knowing the overall mean and one subgroup mean, we can determine the other subgroup mean by working with totals (mean * count).
Given Data / Assumptions:
- Boys = 15, girls = 10
- Overall average = 38.4 kg
- Boys average = 40 kg
Concept / Approach:Total weight of all = overall average * total students. Total of boys = boys average * number of boys. Subtract to get girls’ total, then divide by number of girls for girls’ mean.
Step-by-Step Solution:
Total students = 15 + 10 = 25Overall total = 25 * 38.4 = 960 kgBoys total = 15 * 40 = 600 kgGirls total = 960 - 600 = 360 kgGirls average = 360 / 10 = 36 kgVerification / Alternative check:Check weighted recombination: (600 + 360) / 25 = 960 / 25 = 38.4 kg, matching the given overall average.
Why Other Options Are Wrong:
- 36.5, 35.6, 35, 37 kg: do not satisfy the weighted total when recomputed.
Common Pitfalls:Taking an unweighted mean of 40 and an assumed girls mean without weighting by group sizes.
Final Answer:36 kg