CFA® Level 1: Sample Standard Deviation Calculation | Test Prep

Sample Standard Deviation Calculation

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Question

The sum of the squares of 65 observations equals 862. The sum of the observations equals 93. The sample standard deviation of the observations equals

________.

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Explanations

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A. B. C. D.

C

For N observations, it is easy to show that

sample variance*(N-1) = (sum of squares) - N*(mean^2)

Hence, in this case, sample variance = (862 - 65*(93/65)^2)/64 = 11.39. The standard deviation then equals sqrt(11.39) = 3.37

Note: You should be careful about the difference between population variance and sample variance. The formula for population variance is: population variance*N = (sum of squares) - N*(mean^2)

You can expect an exam question which asks for population variance, with the choices given containing both the population and the sample variances or vice versa.