Outlier Calculator
The fence method: quartiles build the 1.5×IQR gates and every point outside is named by position — with the 3× extreme gates beside, and the doctrine that a flag is a question, never a deletion order.
Outlier Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- One variable at a time — no multivariate or leverage detection
- Fences assume a roughly unimodal core; two-hump lists can hide behind clean gates
In short: Data 12, 13, 15, 16, 14, 13, 15, 14, 98: sorted, Q1 = 13 and Q3 = 15 (the site’s interpolation convention), so the IQR is 2 and the fences sit at 13 − 3 = 10 and 15 + 3 = 18. The 9th point (98) is outside the gate — and outside the extreme fences (7, 21) too, which is the stronger statement. What the page refuses to do is decide for you: a flagged point is a QUESTION — typo? instrument fault? the one real event you built the study for? — and the fences answer none of that. They say only: this value sits where chance, under the box-and-whisker model, rarely puts it.
Formula
low = Q1 − 1.5·IQR · high = Q3 + 1.5·IQR · extreme = 3·IQR (Tukey)
Quartiles use the site’s interpolation convention (the percentile page’s); the fences inherit that choice, and the quartile page shows what the other conventions would say on the same list.
Worked Example
- Paste 4 to 500 values.
- Read the fences and the quartiles they were built from.
- Any flagged points are named by position — the 1-based row you typed.
- Check the extreme gates: outside 3×IQR is the stronger flag, still not a verdict.
Defaults: Q1 13, Q3 15, IQR 2, fences (10, 18); the 9th point (98) is flagged and also outside the extreme gates (7, 21). Clean lists print “no point sits outside the gates”.
Strengths & Limits Of This Model
Where this engine is strong
- Resistant gates: quartiles barely move under the outliers they flag
- Points named by position, with the extreme 3× gate as a severity check
Where it stops
- No z-score or modified-z alternative
- Flags position, never cause — the investigation is yours
Practical Use Cases
Data QC
typo-sized surprises before any average
Lab
runs outside control gates
Teaching
resistant statistics and their limits
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Outlier Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why 1.5×IQR — where does that come from?
Tukey’s box-and-whisker convention: under a normal model, the 1.5 multiplier puts the fences just past the 99.3rd percentile, so a clean sample rarely flags more than a percent or two of points. It is a CONVENTION — the page says so — chosen because it works, not because it is a theorem.
My point was flagged — delete it?
No. A flag is a question: typo, instrument fault, or the one genuine event the whole study exists to catch. Deleting on the flag’s authority launders inconvenient data into tidy conclusions. Investigate the source; only then decide, and say so in the write-up either way.
Why name points by position?
Because you typed rows, not abstractions: the 9th value is the 9th row of your list, and the card hands you its position so the trip back to the source is one step, not a search. Values repeat; positions do not.
Why did nothing get flagged on data I consider weird?
The fences catch TAIL distance, not crowding or bimodality — a list of two tight humps can wear clean gates, and so can a slow drift. Fence checks answer “anyone far from the middle half?” and nothing else; shape questions belong to the skewness and kurtosis pages.
Does an outlier change the fences themselves?
Barely — that is the design. Quartiles have 25% breakdown: nearly a quarter of the data could be garbage before the gates move. The outlier shocks the MEAN and SD (the IQR page’s robustness card shows sd jumping 16.376134 → 40.515566 while IQR holds) but the gates barely flinch — which is why fences use quartiles, not moments.
What is the 3× gate for?
Severity grading. Points outside 3×IQR are extreme even by fence standards — Tukey called them “far out” versus merely “outside”. On the defaults the 9th point clears both gates: (10, 18) flags it, (7, 21) condemns it — and the investigation duty is identical.
Why does this page refuse n < 4?
Quartiles need at least a middle half to define: below 4 values the interpolation convention still computes, but the fences it builds are products of single points, not of a distribution. The floor keeps the gates honest; the outlier page would rather refuse than flag on four numbers.
Are the fences the same as a z-score check?
No — and the difference is the point. z-based rules inherit the mean and SD, which the outlier itself drags: the biggest outlier can hide behind the inflation it causes (masking). The quartile gates are resistant to the very points they flag, which is why this page does not offer the z alternative.