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Outlier/Interquartile Range Calculator

Answer:

Interquartile range: 130.5
Outlier(s): 84
Potential outlier(s): 268, 872

See the outliers and potential outliers highlighted in the sorted data set here:
84, 268, 501, 511, 527, 558, 561, 573, 593, 597, 608, 632, 645, 654, 682, 700, 872


Solution:

The interquartile range, IQR, is the difference between Q3 and Q1. In this data set, Q3 is 649.5 and Q1 is 519. Subtract Q1, 519, from Q3, 649.5. $$ IQR = 649.5 - 519 = 130.5 $$ You can use the 5 number summary calculator to learn steps on how to manually find Q1 and Q3.

To find outliers and potential outliers in the data set, we first need to calculate the value of the inner fences and outer fences. The inner fences are defined by: $$ Q1 - (1.5 \cdot IQR) \text{ and } Q3 + (1.5 \cdot IQR) $$ For this data set: $$ 519 - (1.5 \cdot 130.5) \text{ and } 649.5 + (1.5 \cdot 130.5) $$ $$ \text{Inner fences: } 323.25 \text{ and } 845.25$$

The outer fences are defined by: $$ Q1 - (3 \cdot IQR) \text{ and } Q3 + (3 \cdot IQR) $$ For this data set: $$ 519 - (3 \cdot 130.5) \text{ and } 649.5 + (3 \cdot 130.5) $$ $$ \text{Outer fences: } 127.5 \text{ and } 1041 $$

The inner and outer fences are listed below. Potential outliers are any values in our data set that fall between the inner fences and outer fences, inclusive. Outliers are any values that fall outside of the outer fences.

OutliersOuter fenceInner fenceInner fenceOuter fenceOutliers
127.5323.25845.251041

If there are any outliers in this data set, they will either be less than 127.5 or greater than 1041. Potential outliers will be between 127.5 and 323.25, inclusive or between 845.25 and 1041, inclusive.

In this data set, the outlier(s) is/are: 84
In this data set, the potential outlier(s) is/are: 268, 872

outlier calculator

How To Use the Outlier Calculator

The online outlier calculator applies the interquartile range to determine if there are any outliers or potential outliers in a data set.  Simply enter your data set as a comma separated list into the calculator.

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