Quartile & IQR Calculator
Names the definition, because there are nine of them.
Work out Quartile & IQR. Names the definition, because there are nine of them. Free, with no account and nothing to install.
Comma or space separated. Order does not matter.
Q1, median, Q3
6.75 · 10 · 13.25
IQR 6.5 · 0 outliers
Quartiles have at least nine published definitions that disagree on small samples, which is why the one in use is named rather than left implicit. This uses linear interpolation — R's type 7, and what Excel's QUARTILE and NumPy's percentile both do by default — so the figures here match what those tools return. The interquartile range is the middle half of the data, and it is far more robust than the standard deviation: a single extreme value can double a standard deviation while leaving the IQR untouched. That robustness is exactly why it is used to detect outliers. The fences sit 1.5 IQRs beyond each quartile, and 1.5 is Tukey's convention rather than a statistical threshold. Points beyond them are worth looking at, not deleting — an outlier is a question about the data, and quite often it is the most informative point in the set.
How the Quartile & IQR Calculator works
The five-number summary, the interquartile range and outlier fences, using linear interpolation — R's type 7, and what Excel and NumPy do by default. Quartiles have at least nine definitions that disagree on small samples, so this one is named.
Also known as: find q1 and q3 · interquartile range from data · five number summary calculator · detect outliers in my data
Frequently asked questions
Why do different tools give different quartiles?
Because there are at least nine published definitions, and they disagree whenever the sample size is not a convenient multiple of four. This uses linear interpolation, matching Excel's QUARTILE, R's default and NumPy's percentile.
What is the interquartile range?
The middle half of the data — Q3 minus Q1. It is far more robust than the standard deviation: a single extreme value can double a standard deviation while leaving the IQR untouched.
How are outliers defined here?
Beyond 1.5 interquartile ranges past Q1 or Q3, which is Tukey's convention rather than a statistical threshold. The 1.5 is a rule of thumb, and points beyond it are worth looking at rather than removing.
Should I delete outliers?
Almost never on statistical grounds alone. An outlier is a question about the data — a measurement error, a different population, or the most informative point in the set. Deleting first and asking later is how findings get manufactured.
What is a five-number summary?
Minimum, Q1, median, Q3 and maximum — the five values a box plot draws. It describes a distribution's centre, spread and skew without assuming any particular shape.
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