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At a local yoga studio, 80% of the members are women and 20% of the members are men. The average age of the women is 30 and the average age of the men is 40. What is the average age of all the members?

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Question:

A
32

explanation

This is a weighted average problem, in which the average age of the women carries a weight of 80% and the average age of the men carries a weight of 20%. The combined average age will be the sum of the contribution of each group; which is found by multiplying the group’s average by its weight.

Begin by finding the women’s contribution to the overall average (recall that 80% = 0.8): 0.8 * 30 = 24

Next, find the men’s contribution: 0.2 × 40 = 8

Combine these to find the overall average: 24 + 8 = 32

Notice that this combined average is between the average age of the women (30) and the average age of the men (40), which makes sense because both groups are contributing to the overall average.

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