outlier

An outlier is an observation that diverges markedly from the other observations in a data set. The designation is relative to the distribution, model, and purpose of analysis; an apparent outlier in one context may be a valid observation in another. Outliers can indicate variability in the population, measurement error, data entry mistakes, or rare events.

In statistics, outliers can distort summary statistics and model estimates, especially the mean and linear regression coefficients. They are common in many domains, including finance, biology, sensor data, and social science. Distinguishing between data errors and legitimate extreme values is a key data-quality task.

Detection methods include graphical approaches such as boxplots and scatterplots, as well as quantitative criteria. The IQR rule defines outliers as observations below Q1 minus 1.5 times IQR or above Q3 plus 1.5 times IQR. Z-scores or modified z-scores using the median absolute deviation can identify extreme values. Statistical tests such as Grubbs' test or Dixon's Q test are applied in small samples, while robust methods and machine learning algorithms perform anomaly detection in larger data sets.

Handling outliers depends on the context. They may be corrected if they result from errors, transformed (for example by log or square root transformation), or excluded from analysis. Alternatively, robust statistical methods and models that are less sensitive to extreme values, such as median-based summaries or robust regression, can be used. Documentation of decisions regarding outliers is essential for reproducibility.