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 <math>11</math> games of the season. If his team scores <math>40</math> in the <math> | + | Billy's basketball team scored the following points over the course of the first <math>11</math> games of the season. If his team scores <math>40</math> in the <math>12^{th}</math> 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>\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== | ||
===Solution 1=== | ===Solution 1=== | ||
| − | When they score a < | + | When they score a <math>40</math> on the next game, the range increases from <math>73-42=31</math> to <math>73-40=33</math>. This means the <math>\boxed{\textbf{(A) } \text{range}}</math> increased. |
| + | |||
| + | Note: The range is defined to be the difference of the largest element and the smallest element of a set. | ||
===Solution 2=== | ===Solution 2=== | ||
| − | Because < | + | Because <math>40</math> 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 <math>\boxed{\textbf{(A)}~\text{range}}</math>, may increase. |
| + | |||
| + | ==Video Solution (HOW TO THINK CRITICALLY!!!)== | ||
| + | https://youtu.be/3_D17-g3K-M | ||
| + | |||
| + | ~Education, the Study of Everything | ||
| + | |||
| + | |||
| + | ==Video Solution== | ||
| + | https://www.youtube.com/watch?v=QyBp_12cdGo&list=PL9t_YdPye18V_epxUUbwHTQNeHYBo7a1-&index=9&ab_channel=WhyMath | ||
| + | |||
| + | ~savannahsolver | ||
| + | ==See Also== | ||
{{AMC8 box|year=2015|num-b=4|num-a=6}} | {{AMC8 box|year=2015|num-b=4|num-a=6}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 19:52, 12 May 2023
Contents
Problem
Billy's basketball team scored the following points over the course of the first 
games of the season. If his team scores 
in the 
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.
Note: The range is defined to be the difference of the largest element and the smallest element of a set.
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.
Video Solution (HOW TO THINK CRITICALLY!!!)
~Education, the Study of Everything
Video Solution
~savannahsolver
See Also
| 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. 
