The following table shows the percentage (%) distribution of number of members…

Concept

When a category count and its percentage share are known, the grand total equals count ÷ percentage (in decimal form). A subgroup count is found by applying its percentage to the relevant grand total, and female members equal total members minus male members.

Application

1. Club C has 1,764 total members, which is 14% of all members. Therefore, the grand total of members is 1,764 ÷ 0.14 = 12,600.

2. Club E has 576 male members, which is 8% of all male members. Therefore, the grand total of male members is 576 ÷ 0.08 = 7,200.

3. For club A: total members = 21% of 12,600 = 2,646; male members = 21% of 7,200 = 1,512; female members = 2,646 − 1,512 = 1,134.

4. For club B: total members = 33% of 12,600 = 4,158; male members = 32% of 7,200 = 2,304; female members = 4,158 − 2,304 = 1,854.

5. For club C: total members = 1,764; male members = 19% of 7,200 = 1,368; female members = 1,764 − 1,368 = 396.

6. The average number of female members is (1,134 + 1,854 + 396) ÷ 3 = 3,384 ÷ 3 = 1,128.

Cross-check

Multiplying the average by the three clubs gives 1,128 × 3 = 3,384, which equals 1,134 + 1,854 + 396. Hence, the required average is 1,128.