Billy's basketball team scored the following points over the course of the first $11$ games of the season. If his team scores $40$ in the $12^{th}$ game, which of the following statistics will show an increase?
\[42, 47, 53, 53, 58, 58, 58, 61, 64, 65, 73\]
$\textbf{(A) } \text{range} \qquad \textbf{(B) } \text{median} \qquad \textbf{(C) } \text{mean} \qquad \textbf{(D) } \text{mode} \qquad \textbf{(E) } \text{mid-range}$
Solution 1
When they score a $40$ on the next game, the range increases from $73-42=31$ to $73-40=33$.  This means the $\boxed{\textbf{(A) } \text{range}}$ increased.
Note: The range is defined to be the difference of the largest element and the smallest element of a set.

Solution 2
Because $40$ is less than the score of every game they've played so far, the measures of center will never rise. Only measures of spread, such as the $\boxed{\textbf{(A)}~\text{range}}$, may increase.