1. Finding upper and lower outliers Using the 1.5 x IQR Criterion

2. 70,70,73,73,74,75,77,77,79,79,80,81,82,82,82,82,82,83,83,83,83,84,84,85,88,90,91,92,97,100
Q1=77
Q3=84 70 80 90
100
IQR = Q3-Q1 = 84 – 77 = 7

3. 70,70,73,73,74,75,77,77,79,79,80,81,82,82,82,82,82,83,83,83,83,84,84,85,88,90,91,92,97,100
Q1=77
Q3=84 70 80 90
100
IQR = Q3-Q1 = 84 – 77 = 7
1.5 x IQR = 1.5 x 7 = 10.5

4. 70,70,73,73,74,75,77,77,79,79,80,81,82,82,82,82,82,83,83,83,83,84,84,85,88,90,91,92,97,100
Q1=77
Q3=84 70 80 90
100
IQR = Q3-Q1 = 84 – 77 = 7
1.5 x IQR = 1.5 x 7 = 10.5
Q x IQR = = 94.5

5. All numbers above 94.5 are outliers, so 97 and 100 are upper outliers.
70,70,73,73,74,75,77,77,79,79,80,81,82,82,82,82,82,83,83,83,83,84,84,85,88,90,91,92,97,100
Q1=77
Q3=84 70 80 90
100
IQR = Q3-Q1 = 84 – 77 = 7
1.5 x IQR = 1.5 x 7 = 10.5
Q x IQR = = 94.5
All numbers above 94.5 are outliers, so 97 and 100 are upper outliers.

6. All numbers above 94.5 are outliers, so 97 and 100 are upper outliers.
70,70,73,73,74,75,77,77,79,79,80,81,82,82,82,82,82,83,83,83,83,84,84,85,88,90,91,92,97,100
Q1=77
Q3=84 70 80 90
100
IQR = Q3-Q1 = 84 – 77 = 7
1.5 x IQR = 1.5 x 7 = 10.5
Q x IQR = = 94.5
All numbers above 94.5 are outliers, so 97 and 100 are upper outliers.
Q x IQR = = 66.5

7. All numbers above 94.5 are outliers, so 97 and 100 are upper outliers.
70,70,73,73,74,75,77,77,79,79,80,81,82,82,82,82,82,83,83,83,83,84,84,85,88,90,91,92,97,100
Q1=77
Q3=84 70 80 90
100
IQR = Q3-Q1 = 84 – 77 = 7
1.5 x IQR = 1.5 x 7 = 10.5
Q x IQR = = 94.5
All numbers above 94.5 are outliers, so 97 and 100 are upper outliers.
Q x IQR = = 66.5
All numbers below 66.5 are outliers, so there are no lower outliers.

8. All numbers above 94.5 are outliers, so 97 and 100 are upper outliers.
70,70,73,73,74,75,77,77,79,79,80,81,82,82,82,82,82,83,83,83,83,84,84,85,88,90,91,92,97,100
Q1=77
Q3=84
Q3+1.5 x IQR 70 80 90
100
1 x IQR
1.5 x IQR
IQR = Q3-Q1 = 84 – 77 = 7
1.5 x IQR = 1.5 x 7 = 10.5
Q x IQR = = 94.5
All numbers above 94.5 are outliers, so 97 and 100 are upper outliers.
Q x IQR = = 66.5
All numbers below 66.5 are outliers, so there are no lower outliers.

9. All numbers above 94.5 are outliers, so 97 and 100 are upper outliers.
70,70,73,73,74,75,77,77,79,79,80,81,82,82,82,82,82,83,83,83,83,84,84,85,88,90,91,92,97,100
Q1=77
Q3=84
Q3+1.5 x IQR 70 80 90
100
All data points here are outliers; Outliers are marked as dots and not part of the whisker
1 x IQR
1.5 x IQR
IQR = Q3-Q1 = 84 – 77 = 7
1.5 x IQR = 1.5 x 7 = 10.5
Q x IQR = = 94.5
All numbers above 94.5 are outliers, so 97 and 100 are upper outliers.
Q x IQR = = 66.5
All numbers below 66.5 are outliers, so there are no lower outliers.

10. All numbers above 94.5 are outliers, so 97 and 100 are upper outliers.
70,70,73,73,74,75,77,77,79,79,80,81,82,82,82,82,82,83,83,83,83,84,84,85,88,90,91,92,97,100
Q x IQR
Q1=77
Q3=84
no lower outliers
Q3+1.5 x IQR 70 80 90
100
All data points here are outliers; Outliers are marked as dots and not part of the whisker
1 x IQR
1.5 x IQR
IQR = Q3-Q1 = 84 – 77 = 7
1.5 x IQR = 1.5 x 7 = 10.5
Q x IQR = = 94.5
All numbers above 94.5 are outliers, so 97 and 100 are upper outliers.
Q x IQR = = 66.5
All numbers below 66.5 are outliers, so there are no lower outliers.

11. Finding upper and lower outliers Using the 1.5 x IQR Criterion