Question

the interquartile range of the data set is 4.
2, 2, 3, 3, 4, 5, 5, 6, 7, 9, 12
which explains whether or not 12 is an outlier?
twelve is an outlier because it is greater than the sum of 7 and 4.
twelve is an outlier because it is less than the sum of 7 and 6.
twelve is not an outlier because it is greater than the sum of 7 and 4.
twelve is not an outlier because it is less than the sum of 7 and 6.

Explanation:

Step1: Recall the outlier rule

An outlier is a data point that is greater than \(Q_{3}+ 1.5\times IQR\) or less than \(Q_{1}-1.5\times IQR\). Given \(IQR = 4\). Let's assume \(Q_{3}=7\) (since in the data - set \(2,2,3,3,4,5,5,6,7,9,12\), the median of the upper half of the data is \(7\)).

Step2: Calculate \(Q_{3}+1.5\times IQR\)

Substitute \(Q_{3}=7\) and \(IQR = 4\) into the formula \(Q_{3}+1.5\times IQR\). We get \(7+1.5\times4=7 + 6=13\).

Step3: Compare the data point with the upper - bound

We have the data point \(x = 12\). Since \(12<13\) (where \(13\) is \(Q_{3}+1.5\times IQR\)).

Answer:

Twelve is not an outlier because it is less than the sum of \(7\) and \(6\).