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

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==Problem 5==
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==Problem==
  
 
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?
 
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?

Revision as of 12:51, 15 February 2021

Problem

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

The interquartile range is defined as $Q3 - Q1$, which is $43 - 33 = 10$. $1.5$ times this value is $15$, so all values more than $15$ below $Q1$ = $33; - 15 = 18$ is an outlier. The only one that fits this is $6$. All values more than $15$ above $Q3$ = $43; + 15 = 58$ are also outliers, of which there are none so there is only $1 \boxed{\textbf{(B) }}$

See Also

2017 AMC 12B (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 AMC 12 Problems and Solutions

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