Quartile Calculator
Q1, the median, Q3 and the interquartile range — with the outlier fences a box plot draws.
Quartiles cut ordered data into four equal parts.
How the quartile calculator works
Quartiles cut ordered data into four equal parts. Q1 has a quarter of the values below it, Q2 is the median, Q3 has three quarters below.
The interquartile range, Q3 − Q1, spans the middle half. Unlike the standard deviation it is barely affected by extreme values, which is why box plots use it: the whiskers reach to the furthest point within 1.5 × IQR of the box, and anything past that is drawn as an outlier. That 1.5 is a convention from Tukey, not a statistical law.
This page uses the exclusive method, where the median is left out of both halves — the definition Tukey used and the one most textbooks teach. Spreadsheets offer both, which is why two tools can disagree on the same data.
Formula: IQR = Q3 − Q1; fences = Q1 − 1.5·IQR and Q3 + 1.5·IQR
Worked examples
| Inputs | Interquartile range | Note |
|---|---|---|
| Ten values with one outlier | 7 | IQR 7, and 40 lies past the fence at 22.5 |
| A tidy set | 4 | Q1 2.5, Q3 6.5, IQR 4 |
| An odd count | 6 | median 5, IQR 6 |
FAQFrequently asked questions
What is the interquartile range?
Q3 − Q1, the span of the middle half of the data.
How are Q1 and Q3 found?
Sort the data, split at the median, then take the median of each half. This page excludes the median itself from both halves.
Why do Excel and my textbook disagree?
Excel offers QUARTILE.EXC and QUARTILE.INC, which differ in whether the median joins each half. Both are legitimate; they give different answers on small sets.
What counts as an outlier?
Conventionally anything more than 1.5 × IQR beyond Q1 or Q3. It is a rule of thumb, not a test — an outlier by this rule may be perfectly valid data.
Why use IQR instead of standard deviation?
Because it barely moves when an extreme value appears, so it describes skewed data far better.
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.