Statistics
Five-number summary calculator
Enter your data to get all five numbers and the box and whisker plot they describe, with any outliers marked separately.
Separate numbers with commas, spaces or new lines, or paste a spreadsheet column.
Decimals and negatives are fine; write 10:3 for a value that occurs 3 times.
Your results will appear here: the result first, then the rest of the summary and a chart.
Median
13.5
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. To draw the plot itself, or compare several groups side by side, use the box plot calculator.
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.
-
Percentile calculator
Any percentile, not just the quartiles.
-
Mean, median, mode
The centre of the data, three ways.
-
Standard deviation
The spread measure to pair with the mean.
-
Descriptive statistics
The full summary, adding skewness and kurtosis.
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.