Difference between revisions of "2015 AMC 8 Problems/Problem 5"

Billy's basketball team scored the following points over the course of the first 11 games of the season: $$42, 47, 53, 53, 58, 58, 58, 61, 64, 65, 73$$ If his team scores 40 in the 12th game, which of the following statistics will show an increase?

$\textbf{(A) } \text{range} \qquad \textbf{(B) } \text{median} \qquad \textbf{(C) } \text{mean} \qquad \textbf{(D) } \text{mode} \qquad \textbf{(E) } \text{mid-range}$

Solution

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.

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.

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