Interquartile Range (IQR) Calculator
The spread of the middle half of your data — the robust alternative to the standard deviation, and the basis of the outlier rule.
Sort the data, find the quartiles, subtract: IQR = Q3 − Q1.
How the interquartile range (iqr) calculator works
Sort the data, find the quartiles, subtract: IQR = Q3 − Q1. Because it discards the top and bottom quarters entirely, a single extreme value cannot move it, which is what "robust" means.
For normally distributed data the IQR is about 1.349 standard deviations, so dividing by that gives a robust estimate of σ that outliers cannot inflate.
Formula: IQR = Q3 − Q1; robust σ ≈ IQR / 1.349
Worked examples
| Inputs | Interquartile range | Note |
|---|---|---|
| Eight values | 12 | IQR = 15.5 |
| With one extreme value | 25 | the IQR barely moves; the SD explodes |
| Evenly spaced | 4 | IQR = 4 |
FAQFrequently asked questions
What is the interquartile range?
Q3 − Q1 — how wide the middle 50% of your data is.
Why use it instead of the standard deviation?
Because it is robust. One mistyped value can multiply a standard deviation; it barely touches an IQR.
How do I convert IQR to a standard deviation?
For normal data, divide by 1.349. That is a standard robust estimator of σ.
What is quartile skewness?
Whether the upper quarter is wider than the lower one. Zero means symmetric; positive means a longer right tail.
Does the IQR change if I add a constant?
No. Adding shifts every quartile equally, so the difference is unchanged — spread measures ignore location.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Australian Curriculum (ACARA) — Mathematics — the terms and methods taught in Australian schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.