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IAI Actuarial Core Principles · Actuarial Statistics · Purpose and function of data analysis

A dataset of 1,000 policies has 200 with missing income. Among the 800 with income recorded, the mean claim is ₹10,000. Among the 200 missing income, the mean claim is ₹20,000. The analyst deletes the 200 records (complete-case analysis) and uses ₹10,000 as the overall mean. By how much is the estimate of the true overall mean claim biased?

Understated by ₹2,000. The true mean is (800×10,000 + 200×20,000)/1,000 = ₹12,000, while the complete-case estimate is ₹10,000. Missingness is linked to claim size, so deleting those records creates bias that more data would not cure.

  1. AUnderstated by ₹2,000Correct
  2. BOverstated by ₹2,000
  3. CUnderstated by ₹10,000
  4. DUnderstated by ₹2,500
  5. No bias, since the sample is large

Explanation

True mean = (800×10,000 + 200×20,000)/1,000 = (8,000,000 + 4,000,000)/1,000 = 12,000. The estimate is 10,000, so it is understated by 2,000. The missingness is related to claim size, so deletion biases the result and a large sample does not remove this.

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