Problem:
Compute the range of ${-5, 4, 2, -\frac{49}{5}, -9, -2, -2, \frac{32}{5}, -10, \frac{16}{3}, -4, 4, \frac{497}{64}, -\frac{31}{7}, -7}$.
Answer:
\begin{array}{l}
 
\begin{array}{l}
 \text{Find the range of the list}: \\
 \left(-5,4,2,-\frac{49}{5},-9,-2,-2,\frac{32}{5},-10,\frac{16}{3},-4,4,\frac{497}{64},-\frac{31}{7},-7\right)\text{ = }\left(-5,4,2,-\frac{49}{5},-9,-2,-2,\frac{32}{5},-10,\frac{16}{3},-4,4,\frac{497}{64},-\frac{31}{7},-7\right) \\
\end{array}
 \\
\hline
 
\begin{array}{l}
 \text{The }\text{range }\text{of }\text{a }\text{list }\text{is }\text{given }\text{by}: \\
 (\text{largest element})-(\text{smallest element}) \\
\end{array}
 \\
 
\begin{array}{l}
 \left(-5,4,2,-\frac{49}{5},-9,-2,-2,\frac{32}{5},-10,\frac{16}{3},-4,4,\fbox{$\frac{497}{64}$},-\frac{31}{7},-7\right)  \text{We }\text{see }\text{that }\text{the }\text{largest }\text{element }\text{is }\frac{497}{64}: \\
 \frac{497}{64}-(\text{smallest element}) \\
\end{array}
 \\
 
\begin{array}{l}
 \left(-5,4,2,-\frac{49}{5},-9,-2,-2,\frac{32}{5},\fbox{$-10$},\frac{16}{3},-4,4,\frac{497}{64},-\frac{31}{7},-7\right)  \text{We }\text{see }\text{that }\text{the }\text{smallest }\text{element }\text{is }-10: \\
 -(-10)+\frac{497}{64} \\
\end{array}
 \\
 
\begin{array}{l}
 -(-10)+\frac{497}{64}=\frac{1137}{64}: \\
 \fbox{$
\begin{array}{ll}
 \text{Answer:} &  \\
 \text{} & \frac{1137}{64} \\
\end{array}
$} \\
\end{array}
 \\
\end{array}

{'source': 'AMPS', 'file': 'amps/mathematica/counting_and_statistics/range_w_steps/1199.txt'}