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Interquartile range calculator

Measure the width of the middle half of a data set. Enter observations or supply an already calculated Q1 and Q3.

Use commas, spaces or new lines between numbers. Use the same unit for every observation.

First quartile Q1
2.000000
Third quartile Q3
4.000000
Median
3.000000
Interquartile range
2.000000
Quartile deviation (half IQR)
1.000000

Estimates for information only. Not financial, medical, legal or engineering advice. See the Terms.

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How this calculator works

IQR is the difference between the 75th and 25th percentile cut points. It describes central spread without using the distance to the most extreme observations. In data mode, linear interpolation, medians of halves or nearest rank determine the quartiles. In known-quartile mode the tool simply subtracts, so those quartiles should have been calculated using the same method and unit.

Formula

IQR = Q3 - Q1; quartile deviation = (Q3 - Q1)/2.

Worked example

For 1, 2, 3, 4, 5, linear interpolation gives Q1 = 2 and Q3 = 4. IQR is 2 and quartile deviation is 1.

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Frequently asked questions

Can IQR be negative?

No. Ordered quartiles require Q3 to be at least Q1. A negative difference signals reversed or inconsistent inputs.

Can IQR be zero in nonconstant data?

Yes. Ties can make the two quartiles equal even when a few observations differ.

Does IQR identify outliers by itself?

It supplies the spread used in common outlier fences. The outlier tool applies a chosen multiple to Q1 and Q3.

Sources

Written byAmira MansourCalculator writer. Builds and tests Mathulate calculators against published sources.
Reviewed byMarc LefebvreMathematics teacher. Checks each formula and worked example by hand.

Last updated .

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