Enter your data to get all five numbers and the box and whisker plot they describe, with any outliers marked separately.
Separate values with commas, spaces, tabs or new lines — paste a column straight from a spreadsheet and it will parse. Decimals and negatives are fine.
The box spans the middle 50% of the data, from Q1 to Q3, with the median inside it. Whiskers reach the furthest values still within 1.5 IQR of the box; the 1 point beyond that is an outlier.
Show the working, step by step
The five numbers
| Value | Meaning |
|---|---|
| Minimum | The smallest observation |
| Q1 | A quarter of the data lies below it |
| Median | The middle — half above, half below |
| Q3 | Three quarters of the data lies below it |
| Maximum | The largest observation |
Together they cut the data into quarters, so you can see not just where it sits but how it is shaped — which a mean and standard deviation on their own cannot show you.
Reading shape from the summary
- Median centred in the box, whiskers even — roughly symmetric. A mean and standard deviation will describe it well.
- Median near Q1, long right whisker — right-skewed. Common for incomes, waiting times, file sizes.
- Median near Q3, long left whisker — left-skewed. Common for exam scores on an easy test.
- A very wide box — the bulk of the data is genuinely spread out, not just a couple of stragglers.
This is the quickest reliability check there is on whether the 68–95–99.7 rule or a z-score percentile will behave sensibly on your data. Both assume normality; a lopsided box plot says they will not.
A worked example
For 4, 7, 9, 11, 12, 15, 16, 18, 22, 39 — already sorted, n = 10:
- Minimum 4, maximum 39.
- The median falls between the 5th and 6th values: (12 + 15) / 2 = 13.5.
- Q1 = 9.5 and Q3 = 17.5, so the IQR is 8.
- The upper fence is 17.5 + 1.5 × 8 = 29.5, so 39 is an outlier.
Notice the maximum is 39 while the whisker stops at 22. That gap is the plot telling you one value sits well away from the rest — exactly the signal a mean would bury.
Related calculators
-
IQR & outliers
The interquartile range and Tukey fences in detail.
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Percentile calculator
Any percentile, not just the quartiles.
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Mean, median, mode
The centre of the data, three ways.
-
Standard deviation
The spread measure to pair with the mean.
Common questions
What is the five-number summary?
Minimum, first quartile (Q1), median, third quartile (Q3) and maximum. Those five values describe both the centre and the spread of a dataset, and they are exactly what a box plot draws.
How do I make a box and whisker plot from it?
Draw a box from Q1 to Q3 with a line at the median, then extend whiskers to the furthest points within 1.5 × IQR of the box. The plot above is built that way — anything beyond the whiskers is drawn as a separate outlier point.
What does it tell me that the mean and SD do not?
Shape. If the median sits well off-centre in the box, or one whisker is much longer than the other, the data is skewed — and a mean with a standard deviation would hide that completely. Two datasets can share a mean and SD and look nothing alike.
Does the summary include outliers?
The minimum and maximum are the true extremes, outliers included. The whiskers on the plot are different: they stop at the last value inside the fences, which is what makes the outliers visible as separate points.