Returns for the Dayton Company over the last 3 years are shown below.What's the standard deviation of the firm's returns? (Hint: This is a sample,not a complete population,so the sample standard deviation formula should be used.)

A)20.08%
B)20.59%
C)21.11%
D)21.64%
E)22.18%

Question

Returns for the Dayton Company over the last 3 years are shown below.What's the standard deviation of the firm's returns? (Hint: This is a sample,not a complete population,so the sample standard deviation formula should be used.)
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A)20.08% 
B)20.59% 
C)21.11% 
D)21.64% 
E)22.18%

Quizplus · Accepted Answer

To calculate sample standard deviation, we use the formula:

s = √(Σ(xi - x̄)²/(n-1))

Where:
Σ(xi - x̄)² - Sum of squared deviations from the mean
n - number of observations
x̄ - Mean

Using the given data, we can calculate the mean return as:
Mean = (9% + 15% + 21%) / 3 = 15%

We can calculate the sum of the squared deviations from the mean as:
Σ(xi - x̄)² = (9-15)² + (15-15)² + (21-15)² = 216

The number of observations is n = 3

Using the above formula, we get:
s = √(Σ(xi - x̄)²/(n-1)) = √(216/2) = 20.59%

Therefore, the standard deviation of returns for the Dayton Company over the last 3 years is 20.59%. Hence, the correct answer is option B).

Returns for the Dayton Company Over the Last 3 Years