Returns for the Alcoff 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.) $$\begin{array} { r r }
\text { Year } & \text { Return } \
2010 & 21.00 \% \
2009 & - 12.50 \% \
2008 & 25.00 \%
\end{array}$$
A)20.08%
B)20.59%
C)21.11%
D)21.64%
E)22.18%

Question

Returns for the Alcoff 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.) $$\begin{array} { r r } 
\text { Year } & \text { Return } \
2010 & 21.00 \% \
2009 & - 12.50 \% \
2008 & 25.00 \%
\end{array}$$
A)20.08%
B)20.59%
C)21.11%
D)21.64%
E)22.18%

Quizplus · Accepted Answer

To find the standard deviation of the returns, we will use the sample standard deviation formula. First, we need to find the average return, which is:
(21.00% - 12.50% + 25.00%) / 3 = 11.50% / 3 = 3.83%
Next, we need to find the deviations from the average for each year:
2010: 21.00% - 3.83% = 17.17%
2009: -12.50% - 3.83% = -16.33%
2008: 25.00% - 3.83% = 21.17%
Then, we square each deviation and sum them up:
(17.17%^2 + (-16.33%^2) + 21.17%^2) = 1384.30
We divide this sum by n-1 (where n is the number of observations, in this case n=3) and take the square root:
sqrt(1384.30 / 2) = 20.59%
Therefore, the standard deviation of the Alcoff Company's returns over the last 3 years is 20.59%. Answer choice B) is the best choice.

Returns for the Alcoff Company Over the Last 3 Years Year Return 201021.00%2009−12.50%200825.00%\begin{array} { r r } \text { Year } & \text { Return } \\2010 & 21.00 \% \\2009 & - 12.50 \% \\2008 & 25.00 \%\end{array} Year 201020092008​ Return 21.00%−12.50%25.00%​

Returns for the Alcoff Company Over the Last 3 Years $\begin{array} { r r } \text { Year } & \text { Return } \\2010 & 21.00 \% \\2009 & - 12.50 \% \\2008 & 25.00 \%\end{array}$