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Upper and Lower Outlier Fence Calculator — result sheet
Calculate the lower and upper Tukey-style outlier fences from Q1, Q3, and an entered IQR multiplier.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: IQR = Q3 − Q1; lower fence = Q1 − multiplier×IQR; upper fence = Q3 + multiplier×IQR.
A fence is a rule for screening unusually distant observations, not a declaration that a point is erroneous. The multiplier is explicit so a user can use the familiar 1.5-IQR rule or a documented alternative.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- First quartile Q1 — minimum -1000000000; maximum 1000000000
- Third quartile Q3 — minimum -1000000000; maximum 1000000000
- IQR multiplier — minimum 1.0E-6; maximum 1000
Worked example
| Input | Value |
|---|---|
| First quartile Q1 | 7 |
| Third quartile Q3 | 19 |
| IQR multiplier | 1.5 |
IQR is 12; the lower fence is −11 and the upper fence is 37.
Assumptions and limits
- Q1 and Q3 come from a stated quartile convention and are on the same measurement scale.
- The multiplier is a chosen screening rule, not a universal law or a substitute for domain review.
- Observations outside a fence may be valid, influential, rare, or data errors; this page does not classify them.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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