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 $Q_1 - 1.5\times IQR$. Here, assume the median of the data - set divides it into two halves. First, find the median of the data - set $2,2,3,3,4,5,5,6,7,9,12$. There are $n = 11$ data points. The median is the 6th value, so $Q_2=5$. The lower half is $2,2,3,3,4$ and its median $Q_1 = 3$. The upper half is $5,6,7,9,12$ and its median $Q_3=7$. Given $IQR = 4$.

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: $Q_3+1.5\times IQR=7 + 1.5\times4=7 + 6=13$.

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.