Question

the interquartile range of the data set is 4. 2, 2, 3, 3, 4, 5, 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: Calculate quartiles

First, order the data set: 2, 2, 3, 3, 4, 5, 5, 6, 7, 9, 12. The median (Q2) of the whole data - set is the 6th value, so Q2 = 5. The lower half of the data is 2, 2, 3, 3, 4, and its median (Q1) is 3. The upper half of the data is 5, 6, 7, 9, 12, and its median (Q3) is 7.

Step2: Calculate the inter - quartile range (IQR)

IQR=Q3 - Q1. So, IQR = 7 - 3=4.

Step3: Determine the outlier boundaries

The lower outlier boundary is Q1−1.5×IQR = 3−1.5×4=3 - 6=- 3. The upper outlier boundary is Q3 + 1.5×IQR=7 + 1.5×4=7 + 6 = 13.

Step4: Check if 12 is an outlier

Since - 3<12<13, 12 is not an outlier. And 12 is less than the sum of 7 and 6 (7 + 6=13).

Answer:

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