Outlier calculator
Outliers by Tukey’s 1.5 × IQR rule — and the same rule under all nine published quartile definitions, because on some datasets they disagree about whether a value is an outlier at all. Nothing you type here leaves your browser — it is worked out on your own device, so there is nothing to send and nothing to log.
Tukey’s fences, and what they are not
The usual rule is that a value is an outlier if it falls more than 1.5 interquartile ranges below Q1 or above Q3. It comes from John Tukey and it is a convention for drawing attention, not a test. Nothing about it says a flagged value is wrong, a mistake, or safe to delete.
The 1.5 is not derived from anything. Tukey chose it because it worked; 3.0 is often used for “far out” values, and you can change it above.
And the fence moves with the quartile definition
The fence is built from Q1 and Q3, and there are nine published definitions of those. So the same numbers under the same rule give different fences — and sometimes a different answer.
On 13, 21, 29, 30, 34, 55, six of the nine definitions call 55 an outlier and three do not. The split is not a curiosity: type 7, the default in R, numpy and Excel — the one you get without choosing — puts the fence at 48.00 and flags it. Type 8, which Hyndman and Fan recommend in the paper defining all nine, puts it at 58.87 and does not.
Those are the numbers in the box. Change the definition and watch the verdict change. Nothing about the data did.
What to do with one
Look at it. An outlier is a value worth a second glance, and the second glance is the point — it may be a measurement error, a different population, or the most interesting number you have. Deleting it because a fence flagged it is how real effects get thrown away.