skjevhet

Skjevhet is a term used in Norwegian to describe asymmetry in a distribution or a tilt in a set of measurements. In statistics, skjevhet (skewness) refers to the degree to which a probability distribution deviates from symmetry around its center. A symmetrical distribution has skjevhet close to zero. If the right tail is longer or fatter than the left, the distribution is positively skjev (right-skewed). If the left tail is longer, it is negatively skjev (left-skewed). Skjevhet affects how statistics such as the mean and median describe the data; for positively skewed data the mean tends to exceed the median.

Commonly, skjevhet is quantified by the skewness coefficient, based on the third standardized moment: g1 = E[((X-μ)/σ)^3] for the population, with sample versions used in practice. Several estimators exist (Fisher-Pearson, moment-based). Small samples can produce biased estimates of skjevhet.

In data analysis, pronounced skjevhet may motivate data transformations (for example, logarithmic or Box-Cox) to approximate normality, improve model assumptions, or stabilize variance. Alternatively, nonparametric methods or robust statistics may be preferred when skewness is substantial or outliers are present.

Beyond statistics, skjevhet also appears as a broader notion of bias or distortion in data collection, reporting, or interpretation, where systematic skewness can lead to biased conclusions. In economics and social sciences, income and wealth distributions often exhibit positive skjevhet due to a minority with very high values.