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.

Yes, 1.8 and 9.2 are outliers.

Step-by-step explanation:

Given:

Minimum: 1.8

Q1:3.3

Median: 3.8

Q3: 4.5

Maximum: 9.2

Required:

Determine if there are outliers

Solution:

An outlier is any value in the data set that is either higher than (Q3 + 1.5*IQR) or lower than (Q1 – 1.5*IQR)

Let's find the value of (Q3 + 1.5*IQR) and (Q1 – 1.5*IQR).

Interquartile Range (IQR) = Q3 - Q1 = 4.5 - 3.3 = 1.2

Q3 + 1.5*IQR = 4.5 + 1.5*1.2 = 6.3

Q1 – 1.5*IQR = 3.3 - 1.5*1.2 = 5.1

Any value above 6.3 is an outlier.

Any value below 5.1 is also an outlier.

If we are to pick two extreme values as outliers, it would be 1.8 and 9.2.

Therefore, the answer is:

"Yes, 1.8 and 9.2 are outliers."