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. If his team scores 40 in the 12th game, which of the following statistics will show an increase?
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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>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>\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>
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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>
  
 
==Solutions==
 
==Solutions==
 
===Solution 1===
 
===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.
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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.
  
 
===Solution 2===
 
===Solution 2===
  
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.
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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}}$, may increase.
  
  
 
{{AMC8 box|year=2015|num-b=4|num-a=6}}
 
{{AMC8 box|year=2015|num-b=4|num-a=6}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 16:00, 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 $12th game, which of the following statistics will show an increase?

<cmath>42, 47, 53, 53, 58, 58, 58, 61, 64, 65, 73</cmath>$ (Error compiling LaTeX. ! Missing $ inserted.)\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$ (Error compiling LaTeX. ! Missing $ inserted.)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$ (Error compiling LaTeX. ! Missing $ inserted.)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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