the data set shows the numbers of pages in the books on a reading list. 71, 96, 110, 112, 114, 114, 121…

Explanation:

Step1: Arrange data in ascending order

71, 96, 110, 112, 114, 114, 121, 127, 135, 175, 180

Step2: Find median (Q2)

There are 11 data - points. The median is the 6th value, so Q2 = 114.

Step3: Find lower half and Q1

The lower half is 71, 96, 110, 112, 114. The median of the lower half (Q1) is 110.

Step4: Find upper half and Q3

The upper half is 121, 127, 135, 175, 180. The median of the upper half (Q3) is 135.

Step5: Calculate the inter - quartile range (IQR)

IQR=Q3 - Q1 = 135 - 110=25.

Step6: Calculate the lower and upper bounds for non - outliers

Lower bound = Q1−1.5×IQR = 110−1.5×25 = 110 - 37.5 = 72.5 Upper bound = Q3 + 1.5×IQR = 135+1.5×25 = 135 + 37.5 = 172.5

Step7: Identify outliers

Values less than 72.5 or greater than 172.5 are outliers. So 71, 175, 180 are outliers.

Answer:

71, 175, 180