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.) $$\begin{array} { l r }
\text { Year } & \text { Return } \
2013 & 21.00 \% \
2012 & - 12.50 \% \
2011 & 25.00 \%
\end{array}$$
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.) $$\begin{array} { l r } 
\text { Year } & \text { Return } \
2013 & 21.00 \% \
2012 & - 12.50 \% \
2011 & 25.00 \%
\end{array}$$
A) 20.08%
B) 20.59%
C) 21.11%
D) 21.64%
E) 22.18%

Quizplus · Accepted Answer

To calculate the sample standard deviation, first find the mean return: (21% - 12.5% + 25%) / 3 = 11.83%. Then, calculate the squared deviations from the mean, sum them, divide by (n-1) where n is the number of observations, and take the square root: sqrt(((21-11.83)^2 + (-12.5-11.83)^2 + (25-11.83)^2) / 2) = 20.59%.

Returns for the Dayton Company Over the Last 3 Years Year Return 201321.00%2012−12.50%201125.00%\begin{array} { l r } \text { Year } & \text { Return } \\2013 & 21.00 \% \\2012 & - 12.50 \% \\2011 & 25.00 \%\end{array} Year 201320122011​ Return 21.00%−12.50%25.00%​

Returns for the Dayton Company Over the Last 3 Years $\begin{array} { l r } \text { Year } & \text { Return } \\2013 & 21.00 \% \\2012 & - 12.50 \% \\2011 & 25.00 \%\end{array}$