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Difference between revisions of "2017 AMC 12B Problems/Problem 5"

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==Problem 5==
 
==Problem 5==
  
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The data set <math>[6, 19, 33, 33, 39, 41, 41, 43, 51, 57]</math> has median <math>Q2 = 40</math>, first quartile <math>Q1 = 33</math>, and third quartile <math>Q3 = 43</math>. An outlier in a data set is a value that is more than <math>1.5</math> times the interquartile range below the first quartle (<math>Q1</math>) or more than <math>1.5</math> times the interquartile range above the third quartile (<math>Q3</math>), where the interquartile range is defined as <math>Q3 - Q1</math>. How many outliers does this data set have?
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The data set <math>[6, 19, 33, 33, 39, 41, 41, 43, 51, 57]</math> has median <math>Q_2 = 40</math>, first quartile <math>Q_1 = 33</math>, and third quartile <math>Q_3 = 43</math>. An outlier in a data set is a value that is more than <math>1.5</math> times the interquartile range below the first quartle (<math>Q_1</math>) or more than <math>1.5</math> times the interquartile range above the third quartile (<math>Q_3</math>), where the interquartile range is defined as <math>Q_3 - Q_1</math>. How many outliers does this data set have?
  
 
<math>\textbf{(A)}\ 0\qquad\textbf{(B)}\ 1\qquad\textbf{(C)}\ 2\qquad\textbf{(D)}\ 3\qquad\textbf{(E)}\ 4</math>
 
<math>\textbf{(A)}\ 0\qquad\textbf{(B)}\ 1\qquad\textbf{(C)}\ 2\qquad\textbf{(D)}\ 3\qquad\textbf{(E)}\ 4</math>

Revision as of 18:04, 16 February 2017

Problem 5

The data set $[6, 19, 33, 33, 39, 41, 41, 43, 51, 57]$ has median $Q_2 = 40$, first quartile $Q_1 = 33$, and third quartile $Q_3 = 43$. An outlier in a data set is a value that is more than $1.5$ times the interquartile range below the first quartle ($Q_1$) or more than $1.5$ times the interquartile range above the third quartile ($Q_3$), where the interquartile range is defined as $Q_3 - Q_1$. How many outliers does this data set have?

$\textbf{(A)}\ 0\qquad\textbf{(B)}\ 1\qquad\textbf{(C)}\ 2\qquad\textbf{(D)}\ 3\qquad\textbf{(E)}\ 4$

Solution

See Also

2017 AMC 12B (Problems • Answer Key • Resources)
Preceded by
Problem 4 		Followed by
Problem 6
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All AMC 12 Problems and Solutions

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