This five number summary calculator distills a dataset into the box-plot five: minimum, Q1, median, Q3 and maximum — with interquartile range, Tukey fences and any outliers flagged.
The Box Plot, in Five Numbers
Tukey’s five numbers are the most information-dense summary statistics ever boxed: center, spread, and both tails at a glance. The shape they hint at, quantified, is our Skewness Calculator. Part of our Statistics Calculators collection.
Worked Example (Verified)
- 12, 15, 18, 22, 25, 31, 38, 45, 52, 60 (defaults): Min 12 · Q1 18 · Median 28 · Q3 45 · Max 60, IQR = 27, fences −22.5 to 85.5 → no outliers; the median (28) sits left of the box’s center, hinting at right skew
- Symmetry test by eye: median−Q1 vs Q3−median (10 vs 17 here) — the cheaper skew detector that predates formulas
- A single wild value (swap 60 → 600) moves only Max and the fence verdict: quartiles don’t blink — exactly the robustness the five numbers were designed for, and exactly why means need supervision
Quartile Methods — the Honest Footnote
- This tool uses Tukey hinges; Excel’s QUARTILE.INC interpolates, QUARTILE.EXC excludes — small-n results differ by a point or two between them.
- Report which method your course/tool uses before arguing over a decimal.
- For n < 4 the summary is decorative; for grouped/frequency data, use percentile formulas instead.
- The 1.5×IQR fence is a screening convention (≈ ±2.7σ on normal data), not a deletion warrant — investigate outliers, don’t auto-execute them.
Related Tools
- Skewness Calculator — shape in one number
- Standard Deviation Calculator — mean & spread
- Statistics Calculators — the full collection
Frequently Asked Questions
What is the five number summary?
Minimum, first quartile (Q1), median, third quartile (Q3) and maximum — the complete skeleton of a box plot. Defaults here: 12, 18, 28, 45, 60 with IQR = Q3 − Q1 = 27. This calculator adds range, Tukey fences and outlier flags.
How do you find Q1 and Q3?
Split the sorted data at the median; Q1 is the median of the lower half and Q3 the median of the upper half (Tukey’s hinges, used here). Software packages interpolate instead, so tiny differences across tools are method, not error.
What is the IQR used for?
The interquartile range (Q3−Q1) is the spread of the middle 50% — a robust alternative to standard deviation that outliers can’t inflate. It also powers the 1.5×IQR outlier fence: points beyond Q1−1.5·IQR or Q3+1.5·IQR get flagged for investigation.
Five number summary vs mean and SD — which is better?
For skewed data or data with outliers, the five numbers (median-based) describe typical values more honestly; mean/SD win for roughly symmetric data and feed most inferential formulas. Professional summaries often report both — they interrogate the data from two directions.
What does the summary say about shape?
Compare the gaps: if Q3−median ≫ median−Q1, the right tail stretches (right skew); the whiskers (min→Q1 vs Q3→max) tell the tail story further. The defaults lean right on both checks — confirmed numerically by the Skewness Calculator.
Is this five number summary calculator free?
Yes — free, instant, no sign-up.