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Interquartile Range Calculator

Paste raw values to calculate Q1, Q3 and IQR with Interquartile range selected. Choose the quartile convention, read the subtraction, and compare the box plot and other conventions.

8 valuesMedian of halvesInterquartile range1.5 x IQR fences
convention     median of halves, odd centre excludeddata sorted    1  2  3  4  |  5  6  7  8method         Q1 is the median of the lower 4, Q3 the median of the upper 4.Q1 2.5    Q3 6.5IQR            6.5 - 2.5  =  4middle 50%     2.5 to 6.5, holding 4 of the 8 valuessame data under R7 linear interpolation at 1 + (n - 1)pIQR 3.5
18
Q1
2.5
Q3
6.5
IQR
4
Middle 50%
2.5 to 6.5

Box plot on an axis from 1 to 8. Whisker at 1, box from 2.5 to 6.5 with the median at 4.5, whisker at 8. No value is outside the fences.

Quartile convention
What to put first

Q3 minus Q1, the middle 50% of the data, drawn as the box.

Under median of halves, odd centre excluded, 8 values give Q1 2.5 and Q3 6.5, an interquartile range of 4.

Commas, spaces, tabs, semicolons and new lines all separate values, so a column copied from a spreadsheet pastes straight in, and up to 10,000 values are read at a time. Figures on screen are rounded to six decimal places; the arithmetic itself keeps full double precision. Nothing you type leaves this browser.

Worked examples

  • 1 to 8, median of halveseven count, halves are clean
    Q1 2.5, median 4.5, Q3 6.5, IQR 4
  • Same data under R7linear interpolation
    Q1 2.75, median 4.5, Q3 6.25, IQR 3.5
  • 1, 2, 3, 4, 5, 6, 7, 100the fences decide
    Fences -3.5 and 12.5: 100 listed outside, kept in the data

Where the conventions disagree

The same 8 values under all four conventions. They agree on the median, always. Where they differ, it is on Q1 and Q3.

Q1, median, Q3 and IQR under each quartile convention
ConventionQ1MedianQ3IQR
Median of halves (on screen)2.54.56.54
Tukey hinges2.54.56.54
R7 interpolation2.754.56.253.5
R6 interpolation2.254.56.754.5
The convention on screen. Split the sorted data at the median, then take the median of each half. When the count is odd the middle value goes in neither half. Moore and McCabe, the TI-83 and TI-84, and most school textbooks.
Why two calculators disagree. On 1, 2, 3, 4, 5, 6, 7, 8 the median of halves gives Q1 and Q3 of 2.5 and 6.5, an IQR of 4, while R7 interpolation gives 2.75 and 6.25 and an IQR of 3.5. Both are right under the convention that produced them, so the one to use is the one your course, your journal or your software uses. Enter a valid list to compare all four conventions on your own numbers.

Common questions

How is the interquartile range found?
Subtract the first quartile from the third quartile: IQR = Q3 - Q1. The page shows both quartiles and the subtraction.
Can I calculate IQR from just a mean and standard deviation?
This tool requires raw observations. A mean and standard deviation do not determine empirical quartiles without an assumed distribution. Enter the original values to calculate this list's IQR.

Uses browser double-precision arithmetic under the named quartile convention, with ordinary figures rounded to six decimal places and very large or small figures shown in scientific notation. Values outside the 1.5 x IQR fences are listed and kept in the data; a flag alone does not identify a mistake.