Outlier Detection Calculator
Identify outliers in a dataset using Tukey's 1.5×IQR fence method.
Inputs
Number of Outliers
1
Outliers
100
Lower Fence
-2.0000
Upper Fence
10.0000
Step by step
Values used
Data (comma separated) = 1, 2, 3, 4, 5, 6, 100
Lower Fence
LF = Q1 − 1.5 × IQR
Upper Fence
UF = Q3 + 1.5 × IQR
Number of Outliers
= 1
Outliers
= 100
Lower Fence
= -2.0000
Upper Fence
= 10.0000
How it works
Tukey's method flags any data point below Q1 − 1.5×IQR or above Q3 + 1.5×IQR as an outlier. The 1.5 multiplier captures roughly 99.3% of normally-distributed data within the fences.
Formulas
Lower Fence
LF = Q1 − 1.5 × IQR
- Q1
- First quartile
- IQR
- Interquartile range
Upper Fence
UF = Q3 + 1.5 × IQR
- Q3
- Third quartile
- IQR
- Interquartile range
Frequently Asked Questions
Why use 1.5 as the fence multiplier?
John Tukey chose 1.5 because for a normal distribution it captures about 99.3% of data — extreme enough to be meaningful but not so strict as to flag too many points.
Are outliers always errors?
No. Outliers can be legitimate extreme values, data entry errors, or signals of a different process. They should be investigated, not automatically removed.