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:
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==Problem==
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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?
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<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>
If his team scores 40 in the 12th game, which of the following statistics will show an increase?
 
  
<math>
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<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
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\textbf{(B) } \text{median} \qquad
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==Solutions==
\textbf{(C) } \text{mean} \qquad
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===Solution 1===
\textbf{(D) } \text{mode} \qquad
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\textbf{(E) } \text{mid-range}
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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.
</math>
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===Solution 2===
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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.
  
When they score <math>40</math>, 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.
 
==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 16:01, 16 January 2021

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.


2015 AMC 8 (ProblemsAnswer KeyResources)
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

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