Quartile, IQR and Five-Number Summary Calculator
Splits sorted data into four parts. There is more than one accepted way to do this, so four common ones are shown.
Share sends a link that reopens these numbers. Copy details pastes the full breakdown as a list.
The formula
IQR = Q3 − Q1 five-number summary = minimum, Q1, median, Q3, maximum
The interpolation methods place Q1 at position (n − 1) × 0.25 + 1 (inclusive) or (n + 1) × 0.25 (exclusive) in the sorted list. The other two take the median of each half.
What to watch out for
With a lot of data the methods nearly agree. With a short list they can differ noticeably, which is why a textbook, a spreadsheet and a graphing calculator can disagree without any of them being wrong.
Frequently Asked Questions
Why do different calculators give different quartiles?
They use different methods. For 6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49, Q1 is 25.5 by inclusive interpolation and 15 by exclusive interpolation.
Which method should I use?
The one your course, software or colleagues use, so that your figures can be compared with theirs. Say which one you used when you report it.
What does the IQR tell me?
How wide the middle half of the data is. Extreme values do not affect it.