CFA® Level 1 Exam: Calculation of Sample Standard Deviation

Calculation of Sample Standard Deviation

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Question

You are given n = 12, sum of the (X_i) = 2%, sum of the (X_i)^2 = 0.5%%. Find the sample standard deviation.

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Explanations

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A. B. C. D.

C

The sample standard deviation will be the positive square root of the sample variance. The sample variance will be determined using the computational formula [1/

(n-1)] * {sum (as i goes from 1 to n) of (X_i)^2 - (1/n) * [sum (as i goes from 1 to n) of (X_i)]^2}. So we get 1/11 * (0.5 - 1/12*(2^2)) = 1.51%%. The positive square root of 1.51%% is 1.23%.