Question

a group of 20 students are asked to report the number of pets they keep in their house. the results are: 0,0,0,0,0,1,1,1,1,1,1,1,1,2,2,3,4,4,4,21. 1. would any of these values be considered outliers? explain your reasoning.

Explanation:

Step1: Arrange data in ascending order

0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 4, 4, 4, 21

Step2: Calculate quartiles

First, find the median (Q2). Since n = 20 (even), Q2 is the average of the 10th and 11th - ordered values. Q2=$\frac{1 + 1}{2}=1$.
The lower half of the data is 0, 0, 0, 0, 0, 1, 1, 1, 1, 1. The median of the lower - half (Q1) is the average of the 5th and 6th ordered values. Q1=$\frac{0 + 1}{2}=0.5$.
The upper half of the data is 1, 2, 2, 3, 4, 4, 4, 21. The median of the upper - half (Q3) is the average of the 5th and 6th ordered values. Q3=$\frac{3+4}{2}=3.5$.

Step3: Calculate the inter - quartile range (IQR)

IQR = Q3 - Q1 = 3.5−0.5 = 3.

Step4: Determine the boundaries for outliers

Lower boundary = Q1−1.5×IQR = 0.5−1.5×3=0.5 - 4.5=-4.
Upper boundary = Q3 + 1.5×IQR = 3.5+1.5×3=3.5 + 4.5 = 8.

Step5: Identify outliers

The value 21 is greater than the upper boundary of 8. So, 21 is an outlier.

Answer:

Yes, the value 21 is an outlier. The inter - quartile range (IQR) is 3, and the upper boundary for non - outliers is 8. Since 21>8, it is an outlier.