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

An analyst notes that a sample of 5 monthly returns for an Indian equity fund is 2%, 4%, 6%, 8% and 10%. What is the sample standard deviation of these returns (rounded to two decimals)?

The sample standard deviation is 3.16%. The mean is 6%, the sum of squared deviations is 40, and dividing by n minus 1 gives a variance of 10, whose square root is 3.16%. Using n instead gives 2.83%, which is the population measure.

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

Explanation

Mean = 6%. Squared deviations: 16, 4, 0, 4, 16 = 40. Sample variance = 40/(5-1) = 10, so SD = sqrt(10) = 3.16%. Dividing by n gives variance 8 and SD 2.83%, which is the population figure and wrong for a sample.

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