The five-number summary for the lengths of songs, in minutes, performed by a popular music group is given. Minimum: 1 point 8 cap q sub 1 : 3 point 3 Median: 3 point 8 cap q sub 3 : 4 point 5 Maximum: 9 point 2 The shortest song performed by the group is 1 point 8 minutes while the longest three songs are 5 point 7 , 7 point 5 , and 9 point 2 minutes. Are any of these song lengths outliers?
Answer
A
Yes, 7 point 5 and 9 point 2 are outliers.
B
Yes, 1 point 8 and 9 point 2 are outliers.
C
Yes, 5 point 7 , 7 point 5 , and 9 point 2 are outliers.
D
No, none of the lengths are outliers.
Explanation
The interquartile range is 4.5 − 3.3 = 1.2 minutes. The upper outlier fence is Q3 + 1.5(IQR) = 4.5 + 1.5(1.2) = 6.3 minutes, and the lower fence is 3.3 − 1.5(1.2) = 1.5 minutes. The lengths 7.5 and 9.2 exceed the upper fence, while 1.8 and 5.7 are within the fences. Therefore, 7.5 and 9.2 are outliers.
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