IQR Outlier Detection Calculator

How it works

IQR = Q3 − Q1 · Lower fence = Q1 − k·IQR · Upper fence = Q3 + k·IQR (k = 1.5 standard)

Tukey's rule spots outliers using the middle 50% of the data. It finds the first and third quartiles, takes their gap (the interquartile range), and draws fences a multiple of that gap below Q1 and above Q3. Anything past a fence is unusually far from the bulk of the data. Because it relies on quartiles rather than the mean, the method is robust — a single wild value cannot move the fences much, so it reliably catches that same wild value.

Worked example

For 10, 11, 12, 12, 13, 14, 100: Q1 = 11.5, Q3 = 13.5, IQR = 2. With k = 1.5 the fences are 11.5 − 3 = 8.5 and 13.5 + 3 = 16.5. The value 100 lies above 16.5, so it is flagged as the sole outlier.

Sources: Outlier — Tukey fences, Wikipedia

Frequently asked questions