FRM Part I · FRM Exam Part I · Sample Moments
A sample of 4 monthly returns (in percent) is 1, 3, 5, 7. The sample standard deviation using n-1 is closest to which of the following?
The sample standard deviation is about 2.58 percent. The mean is 4, the squared deviations sum to 20, the variance with n-1 = 3 is 6.667, and its square root is 2.58. Using n would wrongly give 2.24.
- A2.58Correct
- B2.24
- C1.83
- D5.00
Explanation
The mean is 4. Squared deviations are 9, 1, 1, 9, summing to 20. Dividing by 3 gives 6.667 and the square root is 2.58. The value 2.24 comes from dividing by n=4 (variance 5), which ignores the degrees-of-freedom correction.
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