StatReason

Outlier Calculator

Flag values that fall unusually far from the rest of your data, using a documented rule rather than a subjective eyeball check, without ever removing anything from your data automatically.

What this answers

This calculator answers "which values in my data, if any, sit far enough from the rest to be worth a closer look?" Flagging is not the same as removal: every flagged value is returned to you as evidence to investigate, never silently deleted from your dataset.

How it is calculated

The default IQR fence method takes the first and third quartiles of your data (using this site's standard Type 7 quantile convention), computes the interquartile range between them, and flags anything below Q1 minus 1.5 times the IQR or above Q3 plus 1.5 times the IQR. The alternative modified z-score method instead measures each value's distance from the median in units of the median absolute deviation (MAD), a center and spread measure that is itself resistant to being distorted by the very outliers it is trying to detect, and flags any value with an absolute modified z-score above 3.5, a widely used threshold.

Worked example

For the values 1, 2, 3, 4, and 100, the IQR fence method computes Q1 and Q3 from the bulk of the data, giving a modest interquartile range, and 100 falls far above the resulting upper fence, so it is flagged while 1 through 4 are not. The modified z-score method reaches the same conclusion here through a different route: the median absolute deviation stays small because only one value is extreme, so 100's modified z-score comfortably clears the 3.5 threshold.

Assumption audit

Calculated from your data: the quartiles and IQR (or the median and MAD for the modified z-score method), the resulting fences or threshold, and every value that crosses them.
Evidence to review: whether a flagged value is a data-entry error, a genuinely rare but real observation, or a sign that your data comes from more than one underlying population. This calculator cannot distinguish between those explanations.
You must verify: the real-world context behind any flagged value before deciding what to do with it. A statistical fence is a starting point for investigation, never sufficient justification on its own for deleting a data point.

Common mistakes

The most damaging mistake is treating a flagged value as automatically wrong and deleting it without investigation; a legitimate rare event looks identical to an error using these rules alone. A second common mistake is applying the IQR method to heavily skewed data, where the modified z-score method (or a transformation of the data first) is often a more appropriate choice.

Limitations

Both methods use a fixed, conventional threshold (1.5 times IQR, or a modified z-score of 3.5) rather than one tailored to your specific field or sample size. With very small samples, both the IQR and the MAD can be unstable, so treat flags on small datasets as weaker evidence than the same flags on a larger one.