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Outlier/Interquartile Range Calculator

Answer:

Interquartile range: 121
Outlier(s): 51
Potential outlier(s): 234, 839

See the outliers and potential outliers highlighted in the sorted data set here:
51, 234, 500, 502, 510, 517, 526, 534, 548, 560, 568, 570, 577, 584, 608, 630, 638, 678, 678, 684, 700, 839


Solution:

The interquartile range, IQR, is the difference between Q3 and Q1. In this data set, Q3 is 638 and Q1 is 517. Subtract Q1, 517, from Q3, 638. $$ IQR = 638 - 517 = 121 $$ 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: $$ 517 - (1.5 \cdot 121) \text{ and } 638 + (1.5 \cdot 121) $$ $$ \text{Inner fences: } 335.5 \text{ and } 819.5$$

The outer fences are defined by: $$ Q1 - (3 \cdot IQR) \text{ and } Q3 + (3 \cdot IQR) $$ For this data set: $$ 517 - (3 \cdot 121) \text{ and } 638 + (3 \cdot 121) $$ $$ \text{Outer fences: } 154 \text{ and } 1001 $$

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
154335.5819.51001

If there are any outliers in this data set, they will either be less than 154 or greater than 1001. Potential outliers will be between 154 and 335.5, inclusive or between 819.5 and 1001, inclusive.

In this data set, the outlier(s) is/are: 51
In this data set, the potential outlier(s) is/are: 234, 839

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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