Explanation

This is a population variance calculation since we have data for the entire population (all 5 managers).

Step 1: Calculate the population mean (μ)

$$\mu = \frac{\sum X_i}{N} = \frac{0.24 + 0.26 + 0.30 + 0.18 + 0.20}{5} = \frac{1.18}{5} = 0.236$$

Step 2: Calculate squared deviations from the mean

$$(0.24 - 0.236)^2 = (0.004)^2 = 0.000016$$ $$(0.26 - 0.236)^2 = (0.024)^2 = 0.000576$$ $$(0.30 - 0.236)^2 = (0.064)^2 = 0.004096$$ $$(0.18 - 0.236)^2 = (-0.056)^2 = 0.003136$$ $$(0.20 - 0.236)^2 = (-0.036)^2 = 0.001296$$

Step 3: Sum the squared deviations

$$0.000016 + 0.000576 + 0.004096 + 0.003136 + 0.001296 = 0.00912$$

Step 4: Calculate population variance

$$\sigma^2 = \frac{\sum (X_i - \mu)^2}{N} = \frac{0.00912}{5} = 0.001824$$

Key Points:

• This is population variance (divide by N = 5)
• For sample variance, we would divide by (n-1) = 4
• The result 0.001824 corresponds to option A