# 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.

Interquartile range: 154.5

Outlier(s):
55

Potential outlier(s):
161

See the outliers and potential outliers highlighted in the sorted data set here:

55, 161, 502, 505, 520, 527, 543, 576, 576, 579, 603, 616, 620, 645, 677, 679, 683, 686, 696, 869

The interquartile range, IQR, is the difference between Q3 and Q1. In this data set, Q3 is 678 and Q1 is 523.5. Subtract Q1, 523.5, from Q3, 678. $$ IQR = 678 - 523.5 = 154.5 $$ 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: $$ 523.5 - (1.5 \cdot 154.5) \text{ and } 678 + (1.5 \cdot 154.5) $$ $$ \text{Inner fences: } 291.75 \text{ and } 909.75$$

The outer fences are defined by: $$ Q1 - (3 \cdot IQR) \text{ and } Q3 + (3 \cdot IQR) $$ For this data set: $$ 523.5 - (3 \cdot 154.5) \text{ and } 678 + (3 \cdot 154.5) $$ $$ \text{Outer fences: } 60 \text{ and } 1141.5 $$

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.

Outliers | Outer fence | Inner fence | Inner fence | Outer fence | Outliers |

60 | 291.75 | 909.75 | 1141.5 |

If there are any outliers in this data set, they will either be less than 60 or greater than 1141.5. Potential outliers will be between 60 and 291.75, inclusive or between 909.75 and 1141.5, inclusive.

In this data set, the outlier(s) is/are:
55

In this data set, the potential outlier(s) is/are:
161

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.