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…

Explanation:

Step1: Recall outlier - rule

An outlier in a data - set is a value that is greater than $Q_3+1.5\times IQR$ or less than $Q_1 - 1.5\times IQR$, where $IQR$ is the inter - quartile range, $Q_1$ is the first quartile and $Q_3$ is the third quartile. In a simple way, if we assume the upper - bound for non - outliers is $Q_3 + 1.5\times IQR$. Given $IQR = 4$. Let's assume the third quartile $Q_3=7$ (a common way to estimate quartiles for small data - sets).

Step2: Calculate the 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.