FRM Part I · FRM Exam Part I · Sample Moments
An analyst records five monthly returns (in %): 2, 4, 6, 8, 10. She wants an estimate of the variance of the underlying return distribution from this sample. Which value is the unbiased sample variance?
The unbiased sample variance is 10.0. The deviations from the mean of 6 sum in squares to 40, and dividing by n-1 = 4 corrects the downward bias that arises from estimating the mean from the same data. Dividing by 5 would give 8.0.
- A8.0
- B10.0Correct
- C6.4
- D12.5
Explanation
Mean = 6. Squared deviations: 16, 4, 0, 4, 16 = 40. Unbiased sample variance divides by n-1 = 4, giving 10.0. Dividing by n gives 8.0, which is the biased estimator and understates the population variance on average.
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