Five Number Summary Calculator
Enter a list of numbers to get the minimum, Q1, median, Q3, and maximum — with a box plot and full step-by-step working.
Five number summary explained, step by step
The five number summary is a compact, robust description of a dataset: min · Q1 · median · Q3 · max. Unlike the mean and standard deviation, a single extreme value shifts only the min or max — it barely moves the middle three, which is why this summary is preferred for skewed data. Each card below walks through one piece of the workflow this calculator runs.
1. The five values that summarise a dataset
Min and max mark the extremes. Q1 sits a quarter of the way in, Q3 three-quarters in, and the median (Q2) is dead centre. Together the five values split sorted data into four groups of roughly equal size.
2. Exclusive method — median of each half
Sort. If n is odd, drop the overall median before splitting so each half has the same size. Q1 is the median of the lower half; Q3 is the median of the upper half. TI-83/84 calculators and this site's Percentile page use the same method.
3. IQR — spread of the middle 50%
IQR = Q3 − Q1 captures how wide the middle 50% of the data is. Unlike range (max − min), a single stray value can't move it. When median sits closer to Q1, the distribution is right-skewed; closer to Q3, it's left-skewed.
4. Reading the box plot
The box spans Q1–Q3; the line inside is the median; whiskers reach min and max. A roughly symmetric box with the median in the middle means a symmetric distribution. A lopsided box or median stuck near one end signals skew.
A real statistical nuance worth stating outright: there are at least nine defined methods for computing quartiles. Excel's QUARTILE.INC uses linear interpolation and includes the median in both halves; some textbooks use an inclusive median-of-halves. For small samples these methods can give slightly different Q1 and Q3 values. All are mathematically valid — they just draw the cut-points in slightly different places. If your textbook or software gives a different number, that's why. See the Percentile & Quartile Calculator on this site for the same exclusive method.
Five number summary vs standard deviation
The two most common ways to summarise a dataset are:
- Median + IQR (from the five number summary) — position-based. Unaffected by extreme values. Best for skewed data or when outliers are present.
- Mean + standard deviation — magnitude-based. A single very large or very small value pulls both the mean and the standard deviation. Best when data is roughly symmetric with no strong outliers.
If you suspect outliers, first flag them with the Outlier Detector (Tukey's 1.5·IQR rule), then compare the median/IQR you get here against the mean and standard deviation from the Standard Deviation Calculator. A large gap between the mean and the median is a strong hint that outliers are distorting the mean.
Common mistakes
- Forgetting to sort. Min, Q1, median, Q3 and Max are all positional — they only make sense on sorted data. Reading them off unsorted data gives wrong answers.
- Assuming there's one true quartile. Different tools use different methods. If two calculators disagree on Q1 for the same data, both can be correct — check which method each uses.
- Including the median in both halves for odd n. The exclusive method drops the overall median before splitting; the inclusive method keeps it in both halves. Pick one and stick with it.
- Confusing IQR with range. Range = Max − Min (uses only the two extreme values). IQR = Q3 − Q1 (uses the middle 50% and ignores extremes).
Features of this calculator
- Computes all five summary values plus IQR in one step.
- Renders a labeled SVG box plot with whiskers to min/max and a median line inside the box.
- Shows the sorted data and every calculation step in a collapsible working panel.
- Uses the exclusive quartile method — the same method as the Percentile & Quartile Calculator on this site — so numbers agree across pages.
- Accepts messy input: commas, spaces, tabs, line breaks, currency symbols and thousand separators are cleaned automatically.
- Copy the result as text or download the box plot as a PNG.
Frequently asked questions
+What is the five number summary used for?
To summarise a dataset's center and spread using position-based statistics that aren't distorted by outliers, and to draw a box plot for quick visual comparison of one or more distributions.
+Which quartile method does this page use?
The exclusive method (median-of-halves), matching the Percentile & Quartile Calculator on this site and the method used by TI-83/84 calculators.
+Why does Excel give me a different Q1?
Excel's QUARTILE.INC and PERCENTILE.INC use linear interpolation across all values, which includes the median in both halves. For small samples that produces a slightly different cut-point than the exclusive method used here. Both answers are correct under their respective definitions.
+How many values do I need?
At least 4. With fewer values the halves are too small to have a meaningful median.
+Do outliers change the five number summary?
They change the min and max directly, but Q1, the median, and Q3 barely move — that's the whole point of using a robust summary. To flag outliers explicitly, use the Outlier Detector.
+How is the box plot drawn?
The box spans Q1 to Q3, with a line inside at the median. Whiskers extend to the minimum and maximum. This is the classic Tukey box plot without outlier separation — for outlier-aware whiskers, use the Percentile & Quartile Calculator's box plot.