Calculation Explanation

Step 1: Calculate the Mean

$$\text{Mean} = \frac{(0.12 + 0.13 + 0.05 + 0.04 + 0.20)}{5} = \frac{0.54}{5} = 0.108 \text{ or } 10.8\%$$

Step 2: Calculate Deviations and Squared Deviations

Step 3: Calculate Sample Standard Deviation

$$\text{Sample Standard Deviation} = \sqrt{\frac{\sum(X - \text{Mean})^2}{n - 1}} = \sqrt{\frac{0.017080}{4}} = \sqrt{0.00427} = 0.0653 \text{ or } 6.53\%$$

Key Points:

• We use n-1 in the denominator because this is a sample standard deviation (not population)
• The sample standard deviation is an unbiased estimator of the population standard deviation
• The calculation follows the formula: $s = \sqrt{\frac{\sum(x_i - \bar{x})^2}{n-1}}$