# Difference between revisions of "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 $12^{th}$ game, which of the following statistics will show an increase?

$$42, 47, 53, 53, 58, 58, 58, 61, 64, 65, 73$$

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

## Solutions

### 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.

### 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.

## Video Solution

~savannahsolver

 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