At a health club, 40% of the members are women and 60% of the members are men.…
2026
At a health club, 40% of the members are women and 60% of the members are men. If the average age of the men is 55 years and the average age of the women is 41 years, what is the average age (in years) of all the members?
Answer: A. 49.4 — ConceptA weighted average combines each group mean in proportion to that group’s share. If the shares are w₁ and w₂ and the group means are a₁ and a₂, the…
- A.
49.4
- B.
56.2
- C.
41.7
- D.
60.2
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Show answer & explanation
Correct answer: A
Concept
A weighted average combines each group mean in proportion to that group’s share. If the shares are w₁ and w₂ and the group means are a₁ and a₂, the combined mean is w₁a₁ + w₂a₂, where w₁ + w₂ = 1.
Equivalently, choose a convenient total, convert each percentage into a count, add the groups’ total-age contributions, and divide by the total count.
Application
Assume there are 100 members. Then there are 60 men and 40 women.
The men’s total-age contribution is 60 × 55 = 3300, and the women’s contribution is 40 × 41 = 1640.
The combined total-age contribution is 3300 + 1640 = 4940.
Therefore, the average age is 4940 ÷ 100 = 49.4 years.
Cross-check
The two group means differ by 55 − 41 = 14 years. Starting from the men’s mean, the 40% share of women lowers the combined mean by 0.40 × 14 = 5.6 years, giving 55 − 5.6 = 49.4 years.
Result
The average age of all the members is 49.4 years.