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.)
Year Return 2011 21% 2010 -12.50% 2009 25%
A)20.08%
B)20.59%
C)21.11%
D)21.64%
E)22.18%

Question

Quizplus · Accepted Answer

To calculate the standard deviation of a sample, we use the following formula:
s = sqrt [ Σ(xi - x̄)² / (n - 1) ]
where:
Σ = sum of
xi = each individual value in the sample
x̄ = the sample mean
n = sample size

Using the formula, we can calculate the standard deviation of Dayton Company's returns over the last 3 years:
First, find the mean return:
x̄ = (21% - 12.50% + 25%) / 3 = 11.50%
Next, calculate the variance:
[(21% - 11.50%)² + (-12.50% - 11.50%)² + (25% - 11.50%)²] / 2 
= (9.50%)² + (-24%)² + (13.50%)² / 2
= 90.25% + 576% + 182.25% / 2
= 424%
Finally, find the standard deviation:
s = sqrt [ 424% / (3 - 1) ] = sqrt (424% / 2) = 20.59%
Therefore, the best choice is B, 20.59%.

Returns for the Dayton Company Over the Last 3 Years