skews

Skew is a term used across disciplines to describe asymmetry, bias, or non-alignment. The plural form skews refers to multiple instances or examples of skew in different contexts, ranging from statistics and geometry to data processing and everyday language.

In statistics and probability, skewness measures the asymmetry of a distribution around its mean. A positively skewed distribution has a longer tail on the right, while a negatively skewed one has a longer tail on the left. Skewness can be quantified using moment-based statistics, such as the third standardized moment, and influences modeling choices, data transformations, and interpretation of averages.

In geometry and linear algebra, skew appears in several closely related ideas. Skew lines are lines in three-dimensional space that do not intersect and are not parallel. Skewness also describes skew-symmetric (or antisymmetric) matrices, which satisfy A transpose equals negative A. Such matrices have distinctive properties, including zero diagonal elements and a structure that makes their eigenvalues occur in pure imaginary pairs (and, in even dimensions, symmetric pairings). The collection of n-by-n skew-symmetric matrices has dimension n(n−1)/2.

In data analysis and applied contexts, skew describes bias or distortion in data or results. Skew can arise from sampling methods, measurement errors, or model misspecification. Analysts may apply transformations (for example, logarithmic) or choose robust methods to mitigate the effects of skew on inference and prediction.

In everyday usage, to skew means to tilt or bias something away from an objective stance. Skews as examples illustrate how asymmetry and bias can manifest in diverse areas, from mathematics to practical data interpretation.