Financial Risk Manager Part 1

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Compute the sample standard deviation given the following sample data: ∑x = 31,353, n = 100, ∑x² = 10,687,041

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Explanation:

Calculation Steps

Given:

Step 1: Calculate the sample mean (x̄)

\bar{x} = \frac{\sum x}{n} = \frac{31,353}{100} = 313.53

Step 2: Calculate the sample variance (s²) Using the formula:

s^2 = \frac{1}{(n-1)} \left[ \sum x^2 - n\bar{x}^2 \right]

s^2 = \frac{1}{99} \left[ 10,687,041 - 100 \times (313.53)^2 \right]

s^2 = \frac{1}{99} \left[ 10,687,041 - 100 \times 98,300.8609 \right]

s^2 = \frac{1}{99} \left[ 10,687,041 - 9,830,086.09 \right]

s^2 = \frac{1}{99} \times 856,954.91 = 8,655.9082

Step 3: Calculate the sample standard deviation (s)

s = \sqrt{s^2} = \sqrt{8,655.9082} = 93.0371 \approx 93

Therefore, the sample standard deviation is approximately 93.

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