The interquartile range of the data set is 4. 2, 2, 3, 3, 4, 5, 5, 6, 7, 9, 12 Which explains whether or not 12 is an outlier?
Answer
A
Twelve is an outlier because it is greater than the sum of 7 and 7.
B
Twelve is an outlier because it is less than the sum of 7 and 6.
C
Twelve is not an outlier because it is less than the sum of 7 and 6.
D
Twelve is not an outlier because it is greater than the sum of 7 and 4.
Explanation
The upper outlier fence is the third quartile plus 1.5 times the interquartile range. Here, Q3 is 7 and the IQR is 4, so the fence is 7 + 1.5(4) = 7 + 6 = 13. Since 12 is less than 13, it is not an outlier; choice C gives this explanation.
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