# 2015 AMC 8 Problems/Problem 5

## 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 (Problems • Answer Key • Resources) Preceded byProblem 4 Followed byProblem 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