2015 AMC 8 Problems/Problem 5

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Problem

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 $12th game, which of the following statistics will show an increase?

<cmath>42, 47, 53, 53, 58, 58, 58, 61, 64, 65, 73</cmath>$ (Error compiling LaTeX. ! Missing $ inserted.)\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} $==Solutions== ===Solution 1===

When they score a$ (Error compiling LaTeX. ! Missing $ inserted.)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$ (Error compiling LaTeX. ! Missing $ inserted.)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.


2015 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions

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