How it works
The five-number summary describes a data set with its minimum, first quartile (Q1), median, third quartile (Q3) and maximum. These are the values drawn in a box-and-whisker plot.
The interquartile range (IQR = Q3 − Q1) is the spread of the middle 50% of the data. Because it ignores the extremes, it is a robust measure of spread for skewed data.
Values more than 1.5 × IQR below Q1 or above Q3 are flagged as outliers, following Tukey’s rule. Box plot whiskers extend to the most extreme values that are not outliers.
Formula
IQR = Q3 − Q1 · Lower fence = Q1 − 1.5 × IQR · Upper fence = Q3 + 1.5 × IQR
Questions people ask
Why do different tools give different quartiles?
There are several quartile conventions. This calculator uses the median-of-halves method taught in most intro courses and used by TI calculators; Excel’s QUARTILE.INC interpolates and can differ slightly.
Should I remove outliers?
Not automatically. An outlier may be a data entry error, or a real and important value. Investigate it before deciding, and report what you did.
What does the IQR tell me that the range does not?
The range depends only on the two most extreme values, so one outlier can inflate it. The IQR describes the middle half of the data and is barely affected by extremes.