In a given village there are only three sizes of families: families with 2 members, families with 4 members and families with 6 members. The proportion of families with 2, 4 and 6 members are…
Question and options
In a given village there are only three sizes of families: families with 2 members, families with 4 members and families with 6 members. The proportion of families with 2, 4 and 6 members are roughly equal. A poll is conducted in this village wherein a person is chosen at random and asked about his/her family size. The average family size computed by sampling 1000 such persons from the village would be closest to
- 4
- 4.667
- 4.333
- 3.667
Answer and explanation
Correct answer: B - 4.667
Sampling persons is size-biased: share of persons from 2,4,6-member families is 2:4:6. Expected size = (2*2+4*4+6*6)/12 = 56/12 = 4.667.
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