IQR & Outlier Boundary Calculator
Find Q1, Q3, IQR and outliers using Tukey's 1.5×IQR rule.
How IQR and outlier boundaries work
The interquartile range (IQR) measures the spread of the middle 50% of a dataset, and is the basis for one of the most widely used outlier-detection rules in introductory statistics.
Add every value in your dataset. The calculator sorts them, finds the first quartile (Q1) and third quartile (Q3) using the standard median-of-halves method, and computes the IQR and outlier boundaries using Tukey's 1.5×IQR rule.
Any value below the lower boundary or above the upper boundary is flagged as an outlier — a useful first-pass screen, though always review flagged values in context rather than removing them automatically.
The formula
IQR = Q3 − Q1. Lower bound = Q1 − 1.5×IQR. Upper bound = Q3 + 1.5×IQR.
Sort the data and split it at the median into a lower half and an upper half. Q1 is the median of the lower half; Q3 is the median of the upper half. IQR is their difference, and Tukey's fences extend 1.5 times the IQR beyond each quartile.
Worked example
1, 2, 2, 3, 4, 5, 6, 7, 8, 9, 30
Q1 = 2, Q3 = 8, IQR = 6. Lower bound = 2 − 9 = −7. Upper bound = 8 + 9 = 17. The value 30 falls above the upper bound and is flagged as an outlier.
Frequently asked questions
Why 1.5×IQR specifically?
It's the standard convention from Tukey's original box-plot method — a widely used, if somewhat arbitrary, threshold that flags roughly the most extreme values without being overly aggressive on normally distributed data.
Should I always remove flagged outliers?
No — a flagged value might be a data-entry error worth correcting, or it might be a real, important extreme observation. Investigate before deciding whether to exclude it.
How is this different from Grubbs' test?
Grubbs' test (a separate calculator) is a formal statistical hypothesis test for exactly one suspected outlier, with a p-value. The IQR method is a simpler, distribution-free descriptive screen that can flag multiple values at once.
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