FRM Part I · FRM Exam Part I · Sample Moments
A sample of 5 returns (in %) is: 2, 4, 4, 4, 6. Its sample skewness, defined as the average cubed deviation divided by the cube of the standard deviation, is closest to:
Sample skewness is 0. The mean is 4 and the deviations are -2, 0, 0, 0 and 2, so the cubed deviations cancel exactly. A symmetric sample around its mean has zero third central moment and therefore zero skewness.
- A0Correct
- B1.0
- C-1.0
- D0.5
Explanation
Mean = 20/5 = 4. Deviations: -2, 0, 0, 0, 2. Cubes: -8, 0, 0, 0, 8, summing to 0. Average cubed deviation is 0, so skewness is 0 regardless of the standard deviation used. The data are symmetric around the mean.
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