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Interquartile range calculator

Paste at least four numbers. The tool flags values outside Q1 − 1.5 IQR and Q3 + 1.5 IQR.

Enter 4 to 10,000 numbers.

Number of flagged values: —

Fill in the fields above — the result is computed on this page.

Observations
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Q1
—
Q3
—
IQR
—
Lower fence
—
Upper fence
—
Flagged values
—

Sorted data

Value Outside fence
Fill in the fields above — the result is computed on this page.
What do these numbers mean?
  • A flag is not an instruction to delete a value.
  • Compare the result with a box plot and knowledge of the data source.

Quartiles use R7 interpolation. For small or multimodal data sets, the 1.5 IQR rule may need additional judgement.

How do I use this page?
  1. Paste the data.
  2. Check the quartiles and fences.
  3. Verify flagged observations against their source.

What this page does not do: Quartiles use R7 interpolation. For small or multimodal data sets, the 1.5 IQR rule may need additional judgement.

Further reading

Theory — how are outliers detected using the IQR method?

The IQR rule uses a dataset's quartiles and is resistant to single extreme observations, unlike methods based on the mean and standard deviation. The calculator requires at least four numbers and flags as outliers any values beyond Q1 minus 1.5 IQR or Q3 plus 1.5 IQR — the Tukey fences. Such a value is only a candidate for review, not an automatic data error. Before removing it, its origin must be established — it could be a measurement error, a valid rare case, or part of a different population.

Frequently asked questions

Should I remove every outlier?
No. First determine whether it is an error, a valid rare case or part of another population.
Why does this differ from a Z-score method?
IQR and Z-score rules use different assumptions; IQR does not depend on the mean and standard deviation.

See also

← All calculators

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