Outlier Detection Calculator
Identify outliers in a dataset using Tukey's 1.5×IQR fence method.
About Outlier Detection Calculator
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
Worked example
With the default values below, Outlier Detection Calculator returns Number of Outliers of 1. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Data (comma separated)
- 1, 2, 3, 4, 5, 6, 100
Results
- Number of Outliers
- 1
- Outliers
- 100
- Lower Fence
- -2.0000
- Upper Fence
- 10.0000
Step by step
- 1Values used
- 2Lower Fence
- 3Upper Fence
- 4Number of Outliers= 1
- 5Outliers= 100
- 6Lower Fence= -2.0000
- 7Upper Fence= 10.0000
Assumptions and limits
- The result is derived only from the single input listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
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.