Difference between revisions of "2015 AMC 8 Problems/Problem 5"

(Very Important Notice!)
(9 intermediate revisions by 6 users not shown)
Line 2: Line 2:
 
<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?
 
If his team scores 40 in the 12th game, which of the following statistics will show an increase?
 +
 +
  
 
<math>
 
<math>
Line 10: Line 12:
 
\textbf{(E) } \text{mid-range}
 
\textbf{(E) } \text{mid-range}
 
</math>
 
</math>
 +
===Solution===
 +
 +
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==
  
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.
+
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.
==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}}

Revision as of 19:00, 28 October 2016

Billy's basketball team scored the following points over the course of the first 11 games of the season: \[42, 47, 53, 53, 58, 58, 58, 61, 64, 65, 73\] If his team scores 40 in the 12th game, which of the following statistics will show an increase?


$\textbf{(A) } \text{range} \qquad \textbf{(B) } \text{median} \qquad \textbf{(C) } \text{mean} \qquad \textbf{(D) } \text{mode} \qquad \textbf{(E) } \text{mid-range}$

Solution

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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png