Difference between revisions of "2017 AMC 12B Problems/Problem 5"
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− | The data set <math>[6, 19, 33, 33, 39, 41, 41, 43, 51, 57]</math> has median <math> | + | ==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? | ||
<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> | ||
+ | |||
+ | ==Solution== | ||
+ | The interquartile range is defined as <math>Q3 - Q1</math>, which is <math>43 - 33 = 10</math>. <math>1.5</math> times this value is <math>15</math>, so all values more than <math>15</math> below <math>Q1</math> = <math>33 - 15 = 18</math> is an outlier. The only one that fits this is <math>6</math>. All values more than <math>15</math> above <math>Q3 = 43 + 15 = 58</math> are also outliers, of which there are none so there is only <math>\boxed{\textbf{(B) 1}}</math> outlier in total. | ||
+ | |||
+ | ==See Also== | ||
+ | {{AMC12 box|year=2017|ab=B|num-b=4|num-a=6}} | ||
+ | {{MAA Notice}} |
Latest revision as of 16:42, 27 September 2022
Problem
The data set has median , first quartile , and third quartile . An outlier in a data set is a value that is more than times the interquartile range below the first quartle () or more than times the interquartile range above the third quartile (), where the interquartile range is defined as . How many outliers does this data set have?
Solution
The interquartile range is defined as , which is . times this value is , so all values more than below = is an outlier. The only one that fits this is . All values more than above are also outliers, of which there are none so there is only outlier in total.
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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