Finding upper and lower outliers Using the 1.5 x IQR Criterion

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Presentation transcript:

Finding upper and lower outliers Using the 1.5 x IQR Criterion

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

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

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 Q3 + 1.5 x IQR = 84 + 10.5 = 94.5

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 Q3 + 1.5 x IQR = 84 + 10.5 = 94.5 All numbers above 94.5 are outliers, so 97 and 100 are upper outliers.

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 Q3 + 1.5 x IQR = 84 + 10.5 = 94.5 All numbers above 94.5 are outliers, so 97 and 100 are upper outliers. Q1 - 1.5 x IQR = 77 - 10.5 = 66.5

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 Q3 + 1.5 x IQR = 84 + 10.5 = 94.5 All numbers above 94.5 are outliers, so 97 and 100 are upper outliers. Q1 - 1.5 x IQR = 77 - 10.5 = 66.5 All numbers below 66.5 are outliers, so there are no lower outliers.

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 Q3 + 1.5 x IQR = 84 + 10.5 = 94.5 All numbers above 94.5 are outliers, so 97 and 100 are upper outliers. Q1 - 1.5 x IQR = 77 - 10.5 = 66.5 All numbers below 66.5 are outliers, so there are no lower outliers.

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 Q3 + 1.5 x IQR = 84 + 10.5 = 94.5 All numbers above 94.5 are outliers, so 97 and 100 are upper outliers. Q1 - 1.5 x IQR = 77 - 10.5 = 66.5 All numbers below 66.5 are outliers, so there are no lower outliers.

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 - 1.5 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 Q3 + 1.5 x IQR = 84 + 10.5 = 94.5 All numbers above 94.5 are outliers, so 97 and 100 are upper outliers. Q1 - 1.5 x IQR = 77 - 10.5 = 66.5 All numbers below 66.5 are outliers, so there are no lower outliers.

Finding upper and lower outliers Using the 1.5 x IQR Criterion