Question

The accompanying data show the number of central public libraries in 30 states and the District of Columbia. A summary of the data is shown in the following table. Should the maximum values of this data set be considered potential outliers? Why or why not? You can check your answer by using technology to make a boxplot using fences to identify potential outliers.

Answer 1

Because the maximum value is greater than the right limit, the value is considered a potential outlier

Explanations

What are outliers?

An outlier is data that falls outside the value equivalent to the product of the interquartile range (median) and 1.5.

Before we can determine whether the maximum value is a potential outlier, we need to get the value of 1.5IQR

Given the following parameter:

IQR = 91

1.5 IQR = 1.5(91)

1.5 IQR = 136.5

Since the maximum value of the data which is 623 falls above 1.5 times the interquartile range (623 > 136.5), hence we can conclude that the maximum value of the data is considered a potential outlier because the maximum value is greater than the right limit, the value of considered a potential outlier