Outlier Detector
Find outliers in a data set using Tukey's 1.5×IQR rule. Mild and extreme (3×IQR) outliers listed separately, with a box plot and step-by-step working.
Outlier detection explained, step by step
An outlier is a value that sits unusually far from the rest of the data. It might distort averages, inflate standard deviations, and pull a regression line off course — but it's not automatically an error. Each card below walks through one piece of the workflow this calculator runs.
1. What counts as an outlier
An outlier is a value that sits unusually far from the rest of the data. It might be a genuine extreme (a CEO in a salary sample), a typo (240 typed instead of 24), or a unit mistake (kg mixed into a lb column). The detector's job is to flag candidates for you to investigate — never to silently prune them.
2. Tukey's 1.5·IQR fences — the mild outlier rule
The interquartile range (IQR = Q3 − Q1) is the width of the middle 50%. Anything more than 1.5·IQR beyond Q1 or Q3 is a mild outlier candidate. Because IQR uses only Q1 and Q3, extreme values can't inflate the rule the way they inflate mean ± 3σ.
3. Extreme outliers — 3·IQR fences
Values beyond Q1 − 3·IQR or Q3 + 3·IQR are flagged as extreme outliers. On normal data only about 1 in 250,000 values falls outside these fences — so anything that trips them almost always deserves individual investigation.
4. Investigate — don't automatically delete
Removing every flagged value silently distorts your results and can hide the most important finding in the data. Instead: check the raw source, consider context, report both versions with and without the outlier, and prefer robust methods (median, IQR) when outliers are expected.
Common mistakes
- Deleting outliers by default. Investigate; don't silently prune.
- Using ±3σ on skewed data. The mean and standard deviation are themselves pulled by outliers — that's why IQR fences are the safer default.
- Forgetting to state the method. Different tools use different quartile conventions, so results can vary slightly on small samples.
- Running the rule on tiny samples. With fewer than about 8 values, Q1 and Q3 are jumpy and the fences can flag half the data.
- Confusing mild and extreme. A mild outlier is a candidate; an extreme outlier is almost always worth investigating individually.
Features of this calculator
- Tukey's 1.5·IQR fences applied to Q1 and Q3 — the standard outlier rule
- Separates mild outliers (beyond 1.5·IQR) from extreme outliers (beyond 3·IQR)
- Box plot with individual outlier dots plotted beyond the whiskers
- Full step-by-step working — sorted data, Q1/Q3/IQR, fence formulas, and every flagged value
- Handles pasted spreadsheet data — commas, tabs, currency symbols and thousand separators
- Copy the summary or download the box plot and steps as an image
Frequently asked questions
+Should outliers always be removed?
No. Outliers are candidates for investigation. Remove them only if you can identify a specific cause (typo, unit error, duplicate row) and report your analysis both ways when they might change the conclusion.
+What's the difference between a mild and an extreme outlier?
Mild outliers sit beyond Tukey's 1.5×IQR fences but within 3×IQR of Q1 or Q3. Extreme outliers sit beyond the 3×IQR fences — much further from the bulk of the data and almost always worth individual attention.
+Why 1.5×IQR?
On normal data, about 0.7% of values fall outside the 1.5×IQR fences — unusual without being over-strict. The 3×IQR extreme fence catches roughly 1 in 250,000 normal values, so anything that trips it really is unusual.
+Is this the same rule a box plot uses?
Yes. A standard box plot draws whiskers only to the extreme values inside the 1.5×IQR fences, and plots anything beyond them as individual dots. This calculator does exactly that.
+Does it work on skewed data?
The rule is robust in the sense that Q1, Q3 and IQR aren't distorted by extreme values. But strongly skewed data will still see more points flagged on the long tail — those are usually genuine tail values, not errors. Consider a log transform first for naturally skewed data.