Outlier

An outlier is a data point that lies unusually far from the rest of a dataset. It may reflect real, meaningful variation, a single enormous transaction, a genuine spike in traffic, or it may be a data-entry mistake, a sensor fault, or a unit-conversion error. Deciding which is the case is a judgment call, not a formula.

Common detection rules include flagging any value more than roughly 1.5 times the interquartile range beyond the first or third quartile, or more than two or three standard deviations from the mean, which is equivalent to a large-magnitude z-score. These rules are simple thresholds, not universal truths, and they assume a roughly symmetric distribution; they misfire on skewed data, where legitimately large values get flagged as errors.

Outliers matter because they can distort the mean, standard deviation, and any model fit through least squares, sometimes dramatically, which is why analysts often report both the full-data and outlier-removed versions of a summary statistic. The main pitfall is deleting outliers automatically without investigating them first: removing genuine extreme values can hide the exact signal, fraud, an outage, a viral event, that the analysis was meant to catch. This differs from systematic anomaly detection, which is built to flag such points continuously in live data.