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Math & Statisticsstatistics

Range and IQR Calculator

Range, quartiles and the interquartile range, with outliers flagged by the standard 1.5 rule. The IQR ignores the extremes entirely, which is exactly why it is more useful than the range.

Also called: quartile calculator, outlier calculator.

Separate values with commas or spaces.

Interquartile range
8

The IQR is 8, from Q1 at 4 to Q3 at 12. The full range is 38, from 2 to 40. 1 value(s) fall outside the fences: 40.

First quartile
4
Median
7
Third quartile
12
Range
38
Smallest
2
Largest
40
Lower outlier fence
-8
Upper outlier fence
24
Outliers
1 value(s) fall outside the fences: 40.
How this is calculated
Method and background

How this is calculated

The range is the distance from smallest to largest and is destroyed by a single outlier. The interquartile range covers the middle half, so it describes the bulk of the data regardless of what the extremes do. Tukey's rule marks anything more than one and a half IQRs beyond a quartile as an outlier, which is the convention every box plot uses.

the interquartile range covers the middle half of the data; the 1.5 fences are the standard outlier rule
Q
Quartiles

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

nine values with one extreme

Values
2, 4, 4, 5, 7, 9, 12, 15, 40

Interquartile range8

The range is wrecked by the 40 while the IQR is not

Open this example

a tight set has no outliers

Values
10, 11, 12, 13, 14

Interquartile range2

boundary

Open this example

Method and limits

What it assumes

  • Quartiles by linear interpolation, which is the spreadsheet convention.

What it deliberately does not model

  • Several quartile definitions exist and give slightly different answers on small samples.
  • The 1.5 multiplier is a convention, not a test of significance.

Formula version 1.0.0 · definition 1.0.0 · United States · Report a problem with this calculator

Frequently asked questions

Why use IQR instead of range?
Because one extreme value sets the entire range. The IQR describes the middle half and is unmoved by an outlier, which is why box plots are built on it.