Multiple choice

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

  1. 4

  2. 4.667

  3. 4.333

  4. 3.667
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When sampling people, you are more likely to pick a person from a larger family. The probability of picking a family of size n is proportional to n. The expected value is (2*2 + 4*4 + 6*6) / (2+4+6) = (4+16+36) / 12 = 56 / 12 = 4.667.

AI explanation

Since the number of families of each size is roughly equal, assume there are exactly 100 families of 2 members, 100 families of 4 members, and 100 families of 6 members. This means there are 200 people from the 2-member families, 400 people from the 4-member families, and 600 people from the 6-member families, totaling 1200 people out of 300 families. A randomly sampled person contributes their own family size to the survey, so the average family size reported by the 1200 people will be the total population divided by the number of families, which is 1200 / 300 = 4; however, if the survey strictly samples 1000 people from an infinite or replacement-based model, the probabilities of belonging to each family size are 1/6, 1/3, and 1/2 respectively. Using these probabilities, the expected average family size is (2 * 1/6) + (4 * 1/3) + (6 * 1/2) = 1/3 + 4/3 + 3 = 4.667.

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