FRM Part I · FRM Exam Part I · Sample Moments
A risk manager observes the following sample of 4 daily P&L figures (in $ thousands): -2, 0, 2, 4. Using the sample estimator with n-1 in the denominator, what is the standard error of the sample mean?
The standard error of the sample mean is 1.291. The sample variance is 20/3 = 6.667, giving a standard deviation of 2.582, and dividing by the square root of 4 gives 1.291. It measures the sampling uncertainty of the mean, not the dispersion of the data.
- A0.645
- B1.826
- C0.913Correct
- D1.291
Explanation
Mean = 1. Squared deviations: 9, 1, 1, 9 = 20. Sample variance = 20/3 = 6.667, so sample SD = 2.582. Standard error = 2.582/sqrt(4) = 1.291. Check: the SD/sqrt(n) with n=4 gives 1.291, not 0.913 or others.
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