Question

The five-number summary for the lengths of songs, in minutes, performed by a popular music group is given below.

Minimum: 1.8 Q1:3.3 Median: 3.8 Q3: 4.5 Maximum: 9.2


The shortest song performed by the group is 1.8 minutes while the longest three songs are 5.7, 7.5, and 9.2 minutes.


Are any of these song lengths outliers?


O No, none of the lengths are outliers.


0 Yes, 7.5 and 9.2 are outliers.


Yes, 1.8 and 9.2 are outliers.


O Yes, 5.7, 7.5, and 9.2 are outliers.

Answer 1

1.2

Explanation:

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Answer 2

Yes, 7.5 and 9.2 are outliers

Explanation:

Given the 5 number summary :

Minimum: 1.8

Q1: 3.3

Median: 3.8

Q3: 4.5

Maximum: 9.2

To detect an Outlier use the Relation :

Lower bound : Q1 - 1.5*IQR

IQR = Q3 - Q1 = 4.5 - 3.3 = 1.2

lower bound : 3.3 - 1.5(1.2)

Lower bound = 3.3 - 1.8 = 1.5

Upper bound : Q3 + 1.5*IQR

Upper bound : 4.5 + (1.5 * 1.2)

Upper bound : 4.5 + 1.8 = 6.3

Hence,

1.5≤ x ≤ 6.3

Songs with length 7.5 and 9.2 do not meet the condition and are this outliers