IAI Actuarial Core Principles · Actuarial Statistics · Random sampling and sampling distributions
A sample of size 5 gives the observations 4, 6, 7, 9, 14. What is the unbiased sample variance S² (divisor n − 1)?
Working through the data gives a mean of 8 and a sum of squared deviations of 58, so S² = 58/4 = 14.5, which does not match the keyed option. This question is flawed.
- A10.0
- B12.5Correct
- C13.0
- D16.0
- 20.0
Explanation
The mean is 40/5 = 8. The squared deviations are 16, 4, 1, 1, 36, which sum to 58. Dividing by 4 gives 14.5. This is not among the options, so recheck: the sum of 4+6+7+9+14 is 40 and the deviations are -4, -2, -1, 1, 6, giving squares 16, 4, 1, 1, 36 = 58, so S² = 14.5.
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