Question

multiple choice
which data values of the following set are outliers?
32, 38, 38, 40, 42, 44, 46, 48, 49, 60, 72
remember:
outliers are 1.5 iqrs less than the lower boundary or 1.5 iqrs greater than the upper boundary.
a 72
b 32
c there are no outliers in the data set.

Explanation:

Step1: Arrange data in ascending order

32, 38, 38, 40, 42, 44, 46, 48, 49, 60, 72

Step2: Find the median (Q2)

There are 11 data - points. The median is the 6th value, so Q2 = 44.

Step3: Find the lower half and Q1

The lower half is 32, 38, 38, 40, 42. The median of the lower half (Q1) is 38.

Step4: Find the upper half and Q3

The upper half is 46, 48, 49, 60, 72. The median of the upper half (Q3) is 49.

Step5: Calculate the inter - quartile range (IQR)

IQR=Q3 - Q1 = 49 - 38=11.

Step6: Calculate the lower boundary

Lower boundary = Q1−1.5×IQR = 38−1.5×11 = 38 - 16.5 = 21.5.

Step7: Calculate the upper boundary

Upper boundary = Q3 + 1.5×IQR = 49+1.5×11 = 49 + 16.5 = 65.5.

Step8: Identify outliers

Any value less than 21.5 or greater than 65.5 is an outlier. 72>65.5, so 72 is an outlier.

Answer:

A. 72