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NISM Certifications · NISM-Series-XV: Research Analyst · Fundamentals of Research

An analyst collects the following sample of 5 monthly returns (%) of a stock: 2, 4, 6, 8, 10. What is the sample standard deviation (using n-1)?

The sample standard deviation is 3.16%. The mean is 6, the sum of squared deviations is 40, dividing by n-1 which is 4 gives a variance of 10, and its square root is about 3.16%. Using n would give the population figure of 2.83%.

  1. A2.83%
  2. B3.16%Correct
  3. C6.32%
  4. D10.00%

Explanation

Mean = 6. Squared deviations: 16, 4, 0, 4, 16 = 40. Sample variance = 40/4 = 10, so SD = sqrt(10) = 3.16%. Dividing by n gives variance 8 and SD 2.83%, the population figure, which is wrong for a sample.

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