NISM Certifications · NISM-Series-XV: Research Analyst · Fundamentals of Research
Monthly returns of a stock (in %) over five months are 2, 4, 6, 8 and 10. Treating these as the entire population, what is the standard deviation?
The population standard deviation is 2.83%. The mean is 6, the squared deviations sum to 40, dividing by 5 gives a variance of 8, and its square root is 2.83%. Using n-1 would wrongly give 3.16%.
- A2.00%
- B2.83%Correct
- C3.16%
- D6.00%
Explanation
Mean = 30/5 = 6. Deviations: -4, -2, 0, 2, 4; squares: 16, 4, 0, 4, 16 = 40. Population variance = 40/5 = 8; standard deviation = square root of 8 = 2.83%. The 3.16% figure comes from dividing by n-1 (sample, 40/4 = 10), which is wrong for a population. The 6% option is just the mean.
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