Difference between revisions of "2015 AMC 8 Problems/Problem 5"
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==Problem== | ==Problem== | ||
| − | Billy's basketball team scored the following points over the course of the first 11 games of the season | + | 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> | <cmath>42, 47, 53, 53, 58, 58, 58, 61, 64, 65, 73</cmath> | ||
| − | |||
| − | |||
| − | |||
| − | <math> | + | <math>\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} </math> |
| − | \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} | ||
| − | </math> | ||
==Solutions== | ==Solutions== | ||
Revision as of 14:59, 16 January 2021
Contents
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?
![\[42, 47, 53, 53, 58, 58, 58, 61, 64, 65, 73\]](http://latex.artofproblemsolving.com/4/c/2/4c24d4c07e2a72cf04fa5c16f6d7ec90faad13b5.png)
Solutions
Solution 1
When they score a 
on the next game, the range increases from 
to 
. This means the 
increased.
Solution 2
Because 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 
, may increase.
| 2015 AMC 8 (Problems • Answer Key • Resources) | ||
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
