IAI Actuarial Core Principles · Actuarial Statistics · Random sampling and sampling distributions
A random sample of 5 values from a population gives 4, 7, 9, 12, 8. What is the unbiased estimate of the population variance?
The unbiased estimate of the population variance is 8.50. The mean is 8, the sum of squared deviations is 34, and dividing by n-1=4 gives 8.5. Dividing by 5 would give 6.8, which underestimates the variance on average.
- A8.50Correct
- B6.80
- C7.50
- D8.00
- 34.00
Explanation
Sum=40, mean=8. Deviations squared: 16+1+1+16+0=34. Divide by n-1=4 to get 8.5. Dividing by n gives 6.8, which is biased; 34 is the sum of squares only.
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