Five Number Summary Calculator
Minimum, first quartile, median, third quartile and maximum — everything a box plot draws, with the outlier fences.
The five-number summary splits a sorted dataset into quarters.
How the five number summary calculator works
The five-number summary splits a sorted dataset into quarters. The median is the middle value; Q1 and Q3 are the medians of the lower and upper halves (excluding the median itself when the count is odd — the Tukey method a box plot uses).
The interquartile range Q3 − Q1 holds the middle half of the data, and 1.5 × IQR beyond each quartile gives the fences past which points are drawn as outliers.
Formula: IQR = Q3 − Q1; fences = Q1 − 1.5 IQR, Q3 + 1.5 IQR
Worked examples
| Inputs | Median (Q2) | Note |
|---|---|---|
| Nine values | 12 | median 12, IQR 13 |
| With an outlier | 5 | 100 is flagged |
| An even count | 2.5 | median 2.5 |
FAQFrequently asked questions
What is a five-number summary?
Minimum, Q1, median, Q3 and maximum — the five values a box plot is drawn from.
How are quartiles calculated?
This uses Tukey's method: the median of the lower half and of the upper half, excluding the overall median when the count is odd. Other conventions exist and can differ by a fraction.
What is the IQR?
Q3 − Q1 — the width of the middle 50% of the data. It ignores the tails, which is what makes it robust.
What counts as an outlier?
Conventionally, anything more than 1.5 × IQR beyond a quartile. It is a flag for inspection, not a verdict — outliers are often the most interesting points.
Why not just use the mean and standard deviation?
Because both are pulled hard by extreme values. The five-number summary describes skewed data honestly.
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.