The 18 faculty members in a college math department range in age from 32 to 68. A stemplot follows: The 1.5 × IQR rule would identify an age as a low outlier if it was less than:
A)32 years.
B)28.5 years.
C)19 years.
D)10.5 years.

Question

The 18 faculty members in a college math department range in age from 32 to 68. A stemplot follows:  The 1.5 × IQR rule would identify an age as a low outlier if it was less than:
A)32 years. 
B)28.5 years. 
C)19 years. 
D)10.5 years.

Quizplus · Accepted Answer

The stemplot shows that the lower quartile (Q1) is 42 and the upper quartile (Q3) is 58.

The interquartile range (IQR) is equal to Q3 – Q1 = 58 – 42 = 16.

Using the 1.5 × IQR rule, an observation is considered a low outlier if it is below Q1 – 1.5 × IQR.

Evaluating this expression, we get:

Q1 – 1.5 × IQR = 42 – 1.5 × 16 = 18

Therefore, any age below 18 would be considered a low outlier.

However, the stemplot shows that the youngest age in the department is 32, which is not a low outlier.

Therefore, the answer is D) 10.5 years, but there are no ages in the data that are less than 18.

The 18 Faculty Members in a College Math Department Range