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Outlier Calculator

Detect outliers in a data set using Tukey’s 1.5×IQR rule — see which values fall outside the fences, plus the quartiles and fence bounds.

Data values

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How it works

A value is an outlier if it is below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR, where IQR = Q3 − Q1

This tool applies Tukey’s classic 1.5 × IQR rule to flag outliers. It finds the first and third quartiles, takes their difference as the interquartile range, and builds a fence 1.5 IQRs beyond each quartile. Any value outside that fence is unusually far from the middle of the data and gets flagged. The rule is robust because the quartiles themselves are barely moved by extreme points, so an outlier cannot hide by inflating the very statistic used to detect it.

Worked example

For 10, 12, 14, 15, 16, 18, 55 the quartiles are Q1 = 13 and Q3 = 17, so the IQR is 4. The fences sit at 13 − 6 = 7 and 17 + 6 = 23. The value 55 lies above the upper fence, so it is flagged as an outlier while every other value stays inside.

Sources: Outlier — Wikipedia

Frequently asked questions

Does a flagged outlier mean the data is wrong?

Not necessarily. The rule only marks points that sit far from the middle of the data. An outlier can be a genuine, important observation or a data-entry error — the flag is an invitation to investigate why the value is extreme, not a verdict to delete it.

Why 1.5 times the IQR?

It is John Tukey’s convention, chosen to catch genuine outliers while rarely flagging ordinary values from a roughly normal distribution. Some analyses use 3 × IQR to isolate only "far out" extreme points; 1.5 is the standard for box-plot whiskers.

Is the IQR method better than the z-score method?

It is more robust. Z-score cutoffs rely on the mean and standard deviation, which outliers themselves distort, whereas the quartiles behind the IQR method are hardly affected by extreme values. For skewed data especially, the IQR rule tends to be the safer detector.

Related calculators

Interquartile Range (IQR) Calculator

Find the interquartile range of a data set — the spread of the middle 50% — with Q1, Q3, the median and the 1.5×IQR outlier fences.

Quartile Calculator

Split a data set into quartiles — minimum, Q1, median, Q3 and maximum — with the interquartile range, using linear interpolation.

Five-Number Summary Calculator

Get the five-number summary — minimum, Q1, median, Q3 and maximum — plus the interquartile range and outlier fences for any data set.

Z-Score Calculator

Turn a raw value into a z-score — how many standard deviations it sits above or below the mean — with its percentile under a normal curve.

Standard Deviation Calculator

Paste a list of numbers and get the sample or population standard deviation, variance, mean, standard error, confidence interval, quartiles, z-scores, a frequency table and a histogram, with every step worked out.

For education — check assumptions (sample size, distribution) before using statistics in real decisions.