Re: There are 35 females in a club having an average age of f, and 45 ma
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15 Nov 2024, 16:28
Answer is B
Two important pieces of information:
1) There are more males in the club than females
2) The average age of the female club goers is higher than males.
We can determine the answer without calculations by noticing that Quality A is a weighted average and Quantity B is a unweighted average.
With unweighted averages (Option B), the average ages for males and females are given the same weight regardless of how many males and females there are in each group. It doesn't matter if there are 45 males or 35 females. It's taking an average of the average (average female age + average male age)/2.
With weighted averages (Option A), the calculation accounts for the number of individuals in each group (male and female). Since there are more males in the club and males have a lower average age, the average of all club members (male and female) will be pulled closed towards the average male age since there are more of them. As the average age of the males in the club is less than women, we know Quantity B is greater than Quantity A.
Example in practice w/smaller numbers and no club-goers:
- There is 1 boy (10) and 1 girl (14). The average age and weighted age are equal (10+14)/2 = 12 (average age is right in the middle of 10 and 14)
- 1 more boy enters the group who is also 10. The total average age decreases (10+10+14)/3 = 11.333. The weighted age stays the same (10+14)/2 = 12
- 1 more boy enters the group. They are also 10. The total average age decreases even further (10+10+10+14)/4 =11. The weighted age stays the same (10+14)/4 = 12.