standarddeviationcalculator.net

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 values with commas, spaces, tabs or new lines — paste a column straight from a spreadsheet and it will parse. Decimals and negatives are fine.

Median 13.5
Minimum4
Q1 (25th percentile)9.5
Median (Q2)13.5
Q3 (75th percentile)17.5
Maximum39
IQR (Q3 − Q1)8
Range35
Count (n)10
Lower fence (Q1 − 1.5·IQR)-2.5
Upper fence (Q3 + 1.5·IQR)29.5
Outliers39
Extreme outliers (3·IQR)None
39 4 Q1 9.5 med 13.5 Q3 17.5 29.5

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

ValueMeaning
MinimumThe smallest observation
Q1A quarter of the data lies below it
MedianThe middle — half above, half below
Q3Three quarters of the data lies below it
MaximumThe 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

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:

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.

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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.

Written and reviewed by our editorial team. Last updated . Method and sources: how these numbers are computed.