Interquartile Range Calculator (IQR)

Q1, median, Q3, the interquartile range and 1.5 × IQR outlier fences from your data.

IQR = Q3 − Q1. For 3, 5, 7, 8, 12, 13, 14, 18, 21, 41: the lower half 3, 5, 7, 8, 12 has median Q1 = 7 and the upper half 13, 14, 18, 21, 41 has Q3 = 18, so IQR = 11. The upper fence is 18 + 1.5 × 11 = 34.5, so 41 is an outlier.

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How to use it

  1. Paste your numbers.
  2. Choose the quartile method your course or software uses.
  3. Read Q1, Q3, the IQR, the fences and any outliers.

What you enter

What you get

Formula

IQR = Q3 − Q1 | Fences: Q1 − 1.5 IQR and Q3 + 1.5 IQR

Worked example

Input: 3, 7, 8, 5, 12, 14, 21, 13, 18, 41

Result: Q1 7, Q3 18, IQR 11; outlier 41

41 lies beyond the upper fence of 34.5.

Questions

How do you find the interquartile range?

Sort the data, find the median of the lower half (Q1) and of the upper half (Q3), and subtract: IQR = Q3 − Q1.

Why do calculators give different quartiles?

There are several definitions. TI calculators and most textbooks use the median of each half; Excel's QUARTILE.INC interpolates. Pick the one your class or software uses.

How do you find outliers with the IQR?

Values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR are outliers, the same rule box plots use for their whiskers.

Why use IQR instead of range?

The IQR covers the middle 50% of the data, so one extreme value doesn't distort it.

Related reading

More Statistics

All free tools · By Dr. Zubair Khalid, DVM, MS, PhD.