Problem:
Compute the mean of ${4 \sqrt{3}, -\sqrt{3}, -5 \sqrt{3}, 2 \sqrt{3}, -3 \sqrt{3}, 5 \sqrt{3}}$.
Answer:
\begin{array}{l}
 
\begin{array}{l}
 \text{Find the mean of the list}: \\
 \left(4 \sqrt{3},-\sqrt{3},-5 \sqrt{3},2 \sqrt{3},-3 \sqrt{3},5 \sqrt{3}\right)\text{} \\
\end{array}
 \\
\hline
 
\begin{array}{l}
 \text{The }\text{mean }\text{of }\text{a }\text{list }\text{of }\text{numbers }\text{is }\text{given }\text{by}: \\
 \frac{(\text{sum of elements})}{(\text{number of elements})} \\
\end{array}
 \\
 
\begin{array}{l}
 (\text{sum of elements}) \text{= }4 \sqrt{3}-\sqrt{3}-5 \sqrt{3}+2 \sqrt{3}-3 \sqrt{3}+5 \sqrt{3}: \\
 \frac{4 \sqrt{3}-\sqrt{3}-5 \sqrt{3}+2 \sqrt{3}-3 \sqrt{3}+5 \sqrt{3}}{(\text{number of elements})} \\
\end{array}
 \\
 
\begin{array}{l}
 \text{Counting, }\text{we }\text{see }\text{that }\text{the }\text{list }\text{has }6 \text{elements}: \\
 \frac{4 \sqrt{3}-\sqrt{3}-5 \sqrt{3}+2 \sqrt{3}-3 \sqrt{3}+5 \sqrt{3}}{6} \\
\end{array}
 \\
 
\begin{array}{l}
 4 \sqrt{3}-\sqrt{3}-5 \sqrt{3}+2 \sqrt{3}-3 \sqrt{3}+5 \sqrt{3} \text{= }2 \sqrt{3}: \\
 \frac{1}{6} \left(2 \sqrt{3}\right) \\
\end{array}
 \\
 
\begin{array}{l}
 \frac{2 \sqrt{3}}{6}=\frac{1}{\sqrt{3}}: \\
 \fbox{$
\begin{array}{ll}
 \text{Answer:} &  \\
 \text{} & \frac{1}{\sqrt{3}} \\
\end{array}
$} \\
\end{array}
 \\
\end{array}
{'source': 'AMPS', 'file': 'amps/mathematica/counting_and_statistics/mean_w_steps/4008.txt'}