Outlier Calculator
Find outliers in any data set using the IQR rule (Tukey's fences) or z-scores. Paste your numbers and get bounds and flagged values instantly.
About the Outlier Calculator
This outlier calculator flags unusually large or small values in a numeric data set using the two most common statistical rules. Paste your numbers, choose a method, and it instantly shows the acceptance bounds, every value that falls outside them, and the summary statistics behind the decision.
The IQR rule (Tukey's fences) computes the first and third quartiles and flags anything below Q1 − 1.5×IQR or above Q3 + 1.5×IQR; switch the multiplier to 3 to catch only extreme outliers. The z-score rule instead measures how many sample standard deviations each value sits from the mean and flags values beyond your threshold — 3 is the common convention, 2 is stricter.
The IQR method is robust because quartiles barely move when an outlier is added, while z-scores assume roughly normal data and can be dragged around by the very outliers you are hunting. For small or skewed samples, prefer the IQR rule. All computation happens locally in your browser.
How to Use the Outlier Calculator
- 1Paste your data values, separated by commas, spaces or new lines (at least 4 values).
- 2Choose the IQR rule or z-score rule, and adjust the multiplier or threshold if needed.
- 3Read the lower and upper bounds and the list of flagged outliers.
- 4Copy the outliers or tighten the criteria to compare standard vs extreme outliers.
Frequently Asked Questions
How does the 1.5 IQR rule find outliers?
Take the data 12, 14, 15, 13, 14, 16, 45, 13. Q1 = 13, Q3 = 15.25, so IQR = 2.25. The fences are 13 − 1.5×2.25 = 9.63 and 15.25 + 1.5×2.25 = 18.63. Only 45 falls outside, so it is flagged as an outlier. This is exactly what the calculator computes for your data.
What z-score threshold should I use?
3 standard deviations is the usual convention — in normally distributed data only about 0.3% of values fall beyond ±3 SD, so anything out there is suspicious. Use 2 for a stricter screen (about 5% of normal data lands outside ±2 SD, so expect more false positives) or 2.5 as a middle ground.
IQR or z-score — which method is better?
The IQR rule is more robust: quartiles are barely affected by extreme values, so the fences stay stable. Z-scores use the mean and standard deviation, which the outliers themselves inflate — one huge value can widen the bounds enough to hide itself. Use z-scores mainly for larger, roughly normal samples.
Should I always delete outliers from my data?
No. An outlier can be a data-entry error (delete or fix it) or a genuine extreme observation (often the most interesting point in the set). Standard practice is to investigate each flagged value, document any removal, and report results both with and without the outliers when they materially change conclusions.
Does this tool use population or sample standard deviation?
Sample standard deviation (dividing by n − 1), which is the correct choice when your data is a sample from a larger population — the typical situation. For large n the difference from the population formula is negligible.