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Estimating the average clan size from a survey of people

statisticssize-biased-samplingharmonic-meaninspection-paradox

The people of a country are partitioned into clans of various sizes. To estimate the average size of a clan, a survey picks 1,000 people at random (uniformly over people) and asks each: "How many people are in your clan?"

  1. Why is the ordinary average of the 1,000 answers a biased estimate of the average clan size?
  2. What estimate should you compute from the answers instead?
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A clan of 100 people has 100 chances to be represented in the survey; a clan of 2 has only 2. Big clans are over-sampled in proportion to their size. Correct for that by weighting.

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Why Averaging Averages Gives the Wrong AnswerCorrelation vs CausationDegrees of FreedomThe Inspection Paradox and the Waiting-for-a-Bus TrapRegression to the Mean

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