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 outlier rule

An outlier in a data - set 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. First, assume the data is ordered. The median of the lower half gives $Q_1$ and the median of the upper half gives $Q_3$. For simplicity, if we assume the inter - quartile range ($IQR$) is 4 and we can assume a reasonable $Q_3$ value (since the data is right - skewed, a value around 7 is reasonable). To check for upper outliers, we use the formula $Q_3 + 1.5\times IQR$.

Step2: Calculate the upper - bound for non - outliers

If we assume $Q_3 = 7$ and $IQR=4$, then $Q_3+1.5\times IQR=7 + 1.5\times4=7 + 6=13$.
Since $12<13$, 12 is not an outlier.

Answer:

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