the interquartile range of the data set is 4.\n2,2,3,3,4,5,5,6,7,9,12\nwhich explains whether or not 12 is…

Explanation:

Step1: Recall outlier rule

To check if a value is an outlier, we use the formula $Q_3 + 1.5\times IQR$ (for upper - outliers). Here, $IQR = 4$. First, we need to find $Q_3$. But we can also use a simplified way. We know that to check if a value is an upper - outlier, we can check if it is greater than $Q_3+1.5\times IQR$. A common way in a simple check is to consider a value related to the sum. If we assume some basic relationships, we know that for a non - outlier, a value should be less than a certain sum related to the inter - quartile range. The upper limit for non - outliers can be thought of in a simple case as a value related to the sum of a base value and a multiple of the $IQR$. Here, we can assume a base value of 7 (could be related to $Q_3$ in a simple example) and we know that for non - outliers, the value should be less than $7 + 1.5\times4=7 + 6$.

Step2: Compare the value

We have the value 12. We check if $12<7 + 6$. Since $7+6 = 13$ and $12<13$, 12 is not an outlier.

Answer:

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