Difference between revisions of "2015 AMC 8 Problems/Problem 5"
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− | Billy's basketball team scored the following points over the course of the first 11 games of the season | + | ==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>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== | ||
+ | ===Solution 1=== | ||
− | == | + | 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=== | ||
− | <math> | + | 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. |
− | \textbf{(A) } \text{range} | ||
− | |||
− | |||
− | |||
− | |||
− | </math> | ||
− | |||
− | + | ==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 01:49, 24 February 2023
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?
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
~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.