Outlier

An outlier is an observation unusually distant from the rest of a dataset. It may reflect genuine variation, measurement error, or a different process.

Interquartile range: A measure of statistical dispersion equal to the difference between the third and first quartiles. The 1.5-times-IQR rule flags observations far beyond the central half of a dataset.
Anscombe's quartet: Four datasets with nearly identical summary statistics but markedly different plotted patterns. One dataset contains an influential extreme point, revealing how summaries can conceal outlier effects.
Data cleaning: The process of detecting and correcting inaccurate, incomplete, or inconsistent data. Investigators check whether an extreme value is a recording or processing error before analysis.
Leverage (statistics): A measure of how unusual an observation's predictor values are in a regression dataset. High leverage concerns predictor-space position, not necessarily distance from other observations overall.
Z-score: A standardized value measuring how many standard deviations an observation lies from the mean. Large absolute z-scores mark distant values when mean and standard deviation are suitable summaries.
Cauchy distribution: A heavy-tailed probability distribution whose mean and variance are undefined. Values far from the center can be expected, so distance alone does not establish anomaly.
Influential observation: A data point whose inclusion substantially changes a statistical model's estimates or conclusions. An observation can strongly affect a fit without being unusually distant by itself.
Residual (statistics): The difference between an observed outcome and a model's predicted outcome. A large residual is model-relative; an outlier can be unusual without violating a particular model.
Median absolute deviation: A robust measure of dispersion based on the median of absolute deviations from the median. It supports outlier detection without letting extreme observations strongly distort the scale estimate.
Black swan theory: A framework for rare, high-impact events that are difficult to predict from ordinary experience. Extreme observations can expose failures in models built around familiar ranges.

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