How this instrument works
The five-number summary, introduced by statistician John Tukey as part of exploratory data analysis, condenses an entire data set into exactly five landmark values: the minimum, the first quartile (Q1), the median, the third quartile (Q3), and the maximum. Together they sketch the shape of a distribution at a glance — where it starts, where the middle half sits, where it's centred, and where it ends — without needing every individual value.
It's the specific set of numbers a box-and-whisker plot is built from: the box spans Q1 to Q3 with a line at the median inside it, and the whiskers reach out to the minimum and maximum (or, in some conventions, to the nearest values within 1.5 times the interquartile range, with anything beyond plotted as individual outlier points). This instrument reports the plain minimum and maximum, so the five numbers here are exactly what you need for the simplest, most common version of that chart.
This calculator finds Q1 and Q3 by linear interpolation between the two closest ranked values — the method NIST documents and the one behind spreadsheet software's PERCENTILE.INC function — while the median and the minimum and maximum need no interpolation at all. Reporting all five together, rather than pulling them from separate tools, also guarantees they're internally consistent: the same sorted data set produced every figure.
- Paste or type your numbers into the Data set field — commas, spaces or new lines all work.
- Read the five outputs in order: Minimum, Q1, Median, Q3 and Maximum — they line up exactly as you'd plot a box and whiskers, left to right.
- Use Minimum and Maximum as the whisker ends, Q1 and Q3 as the two edges of the box, and Median as the line drawn inside it.
- Only need the three quartiles without the endpoints? This site's quartile calculator returns Q1, Q2 and Q3 alone; only need min and max? The min-max calculator covers just those two.
Worked example — the eight quiz scores
Take {2, 4, 4, 4, 5, 5, 7, 9}, n = 8, already sorted. The minimum is 2 and the maximum is 9, read straight off the list. Q1 (rank 2.75, between the 2nd and 3rd values, both 4) comes out to 4.0, and Q3 (rank 6.25, between the 6th value 5 and 7th value 7) comes out to 5.5. The median, at rank 4.5 between the 4th value (4) and 5th value (5), is 4.5.
So this instrument reports the five-number summary as Minimum = 2.0000, Q1 = 4.0000, Median = 4.5000, Q3 = 5.5000, Maximum = 9.0000. Plotted as a box plot, the box would run from 4 to 5.5 with a line at 4.5, and whiskers stretching down to 2 and up to 9.
Questions
What are the five numbers in a five-number summary, in order?
Minimum, first quartile (Q1), median, third quartile (Q3), and maximum — always reported in that ascending order, since each one is defined relative to the sorted data set. Together they're the standard input for drawing a box-and-whisker plot.
Who invented the five-number summary and why?
Statistician John Tukey introduced it as part of his broader exploratory data analysis approach, aiming for a quick, robust sketch of a data set's shape that resists distortion from a single extreme value far better than reporting just the mean and standard deviation would.
How is this different from just running the quartile calculator?
The quartile calculator on this site returns only Q1, the median and Q3 — three numbers. This page adds the minimum and maximum to make five, because those two endpoints are exactly what a box plot's whiskers need and the quartile-only tool doesn't provide them.
Does the five-number summary use the same box-plot whisker convention everywhere?
No — this instrument reports the plain minimum and maximum as the two endpoint numbers, which matches the simplest and most traditional box-plot convention. Some statistical software instead caps the whiskers at 1.5 times the interquartile range from the box and marks anything beyond that as a separate outlier point, which is a different (though related) five-number-style summary; check which convention a chart you're comparing against uses.
Can I get the interquartile range from this summary?
Yes — subtract Q1 from Q3 to get it (5.5 - 4.0 = 1.5 in the worked example above). This page doesn't compute that subtraction for you, but it reports both quartiles you need to do it in one step, and a dedicated IQR calculator on this site will do that final subtraction directly.