Statistics
Outlier Calculator
Paste a list of numbers and choose a rule.
The IQR method flags values below Q1 - 1.5 × IQR or above Q3 + 1.5 × IQR (with a 3 × IQR check for extreme outliers); the z-score method flags values more than a chosen number of standard deviations from the mean. Both show the fences, the outliers, and how the mean, median, and standard deviation change once they are removed.
Separate with commas, spaces, or new lines. At least 4 values.
Different textbooks and software locate Q1 and Q3 differently.
1.5 is the standard fence; 3 marks extreme outliers.
Try an example
Result
Outliers
—
- Number of outliers
- —
- Lower fence / limit
- —
- Upper fence / limit
- —
- Mean without outliers
- —
- Median without outliers
- —
- Sample SD without outliers
- —
More details (1 more)
- Original mean
- —
Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the outlier calculator solves
Paste a list of numbers and choose a rule. The IQR method flags values below Q1 - 1.5 × IQR or above Q3 + 1.5 × IQR (with a 3 × IQR check for extreme outliers); the How many standard deviations a value sits above or below the mean. method flags values more than a chosen number of A number saying how far, on average, the data values sit from the mean. from the mean. Both show the fences, the outliers, and how the mean, median, and standard deviation change once they are removed.
Formula
How to use it
- Paste at least four data values.
- Choose IQR fences (robust, works for skewed data) or the z-score rule (assumes roughly normal data).
- Adjust the quartile method, multiplier, or threshold to match your textbook or software.
- Read the outliers and the fences, then compare the original and cleaned summary statistics.
How to read the answer
A value outside the fences is unusually far from the bulk of the data. The IQR rule does not depend on the mean or standard deviation, so a huge outlier cannot hide itself by inflating them; the z-score rule can suffer from that masking effect in small A smaller group taken from a population, used to estimate facts about the whole group.. Compare the original and cleaned means: a large shift means the outliers were driving the average.
Common mistakes and edge cases
- Deleting outliers automatically; investigate first, and report what was removed.
- Using the z-score rule with n under about 12, where |z| can never reach 3.
- Mixing quartile methods between the calculator and your textbook, which can move a borderline value across the fence.
- Treating an IQR of 0 as 'no outliers'; it means the middle half is identical and the rule breaks down.
Worked examples
Two outliers with the IQR rule
Outliers
2, 45
No outliers
Outliers
None
Extreme fence (k = 3)
Outliers
2, 45
z-score rule at 2
Outliers
50
Negative and decimal data
Outliers
-9.9
Undefined: IQR of 0
Outliers
Error
Frequently asked questions
What is the 1.5 IQR rule?+
Compute the interquartile range IQR = Q3 - Q1. Any value below Q1 - 1.5 × IQR or above Q3 + 1.5 × IQR is an outlier. Values beyond 3 × IQR are often called extreme outliers.
How do I find outliers with z-scores?+
Compute z = (x - mean) / SD for each value and flag |z| above a threshold, usually 2, 2.5, or 3. This assumes the data is roughly normal and works poorly for very small samples.
Should I remove outliers?+
Only with a reason. A typo or broken sensor should be fixed or dropped; a genuine extreme value is information. Report results with and without it when in doubt.
Why do different calculators give different fences?+
They locate Q1 and Q3 differently. This calculator lets you pick the exclusive, inclusive, median-split, or Tukey-hinge method so it can match your textbook or software.
How do outliers affect the mean and median?+
The mean moves toward an outlier; the median barely changes. The cleaned summary shows how much each statistic shifts when the flagged values are removed.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
Related calculators
Quartile Calculator
Find Q1, Q2, and Q3 for any data set using the exclusive, inclusive, median-split, or Tukey-hinge method, see how the methods differ, and get the IQR, fences, outliers, and a box plot.
Interquartile Range Calculator
Calculate Q1, median, Q3, and interquartile range from a data list.
Z-score Calculator
Calculate z-score, percentile estimate, and distance from mean using value, mean, and standard deviation.
Five Number Summary Calculator
Find minimum, Q1, median, Q3, maximum, and IQR from a data list with sorted-data steps.
Mean Median Mode Range Calculator
Find mean, median, mode, range, count, sum, minimum, and maximum for a list of numbers with sorted values and steps.
Standard Deviation Calculator
Calculate sample or population standard deviation, variance, mean, and z-score-ready summary statistics from a data list.
Last updated: September 4, 2026