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 out - lier rule

To check if a value is an outlier, we use the formula \(Q_3+ 1.5\times IQR\) for upper - bound outliers (\(Q_3\) is the third quartile and \(IQR\) is the inter - quartile range). Given \(IQR = 4\). First, we need to find \(Q_3\). For the data set \(2,2,3,3,4,5,5,6,7,9,12\), with \(n = 11\) data points, the position of \(Q_3\) is \(\frac{3(n + 1)}{4}=9\)th value. So \(Q_3=7\).

Step2: Calculate upper - bound for non - outliers

The upper - bound for non - outliers is \(Q_3+1.5\times IQR\). Substitute \(Q_3 = 7\) and \(IQR = 4\) into the formula: \(7+1.5\times4=7 + 6=13\).

Step3: Check if 12 is an outlier

Since \(12<13\) (the upper - bound for non - outliers), 12 is not an outlier.

Answer:

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