The following table shows total assets ($ billion) for a small sample of U.S.banks. $$\begin{array} { | l | l | }
\hline{ \text { BANK } } & \text { ASSETS (\$ billion) } \
\hline \text { Bank of New York } & 88 \
\hline \text { Regions Financial } & 80 \
\hline \text { Fifth Third Bank } & 58 \
\hline \text { State Street Bank and Trust } & 92 \
\hline \text { Branch Banking and Trust Company } & 81 \
\hline \text { Chase Bank } & 70 \
\hline \text { Key Bank } & 89 \
\hline \text { PNC Bank } & 84 \
\hline
\end{array}$$ The standard deviation for these data is
A)$12.78 billion.
B)$ 11.27 billion.
C)$ 127.01 billion.
D)$ 21.67 billion.
E)$ 34 billion.

Question

The following table shows total assets ($ billion) for a small sample of U.S.banks. $$\begin{array} { | l | l | } 
\hline{ \text { BANK } } & \text { ASSETS (\$ billion) } \
\hline \text { Bank of New York } & 88 \
\hline \text { Regions Financial } & 80 \
\hline \text { Fifth Third Bank } & 58 \
\hline \text { State Street Bank and Trust } & 92 \
\hline \text { Branch Banking and Trust Company } & 81 \
\hline \text { Chase Bank } & 70 \
\hline \text { Key Bank } & 89 \
\hline \text { PNC Bank } & 84 \
\hline
\end{array}$$ The standard deviation for these data is
A)$12.78 billion.
B)$ 11.27 billion.
C)$ 127.01 billion.
D)$ 21.67 billion.
E)$ 34 billion.

Quizplus · Accepted Answer

To calculate the standard deviation, first find the mean of the assets, then calculate the variance by finding the squared difference from the mean for each bank, average those squared differences, and finally take the square root of that average. The correct calculation leads to a standard deviation of approximately $11.27 billion, indicating option B is correct.

The Following Table Shows Total Assets ($ Billion) for a Small