Skewness quantifies the lack of symmetry in a probability distribution or empirical dataset.
In a perfectly symmetric distribution, the left and right halves mirror each other precisely around the central axis.
Symmetric distributions, like the standard normal distribution, have a theoretical skewness of zero.
Positive skewness, or right-skewness, occurs when the right tail is longer or fatter than the left tail.
In right-skewed data, extreme large values pull the arithmetic mean to the right of the median.
Everyday examples of right-skewed data include individual wealth, insurance claim sizes, and city population totals.
Negative skewness, or left-skewness, occurs when the left tail is longer or fatter than the right tail.
In left-skewed data, extreme small values pull the arithmetic mean to the left of the median.
Examples of left-skewed data include human lifespan in developed nations and retirement age across formal employment.
The sample skewness coefficient is calculated using the third standardised moment of the distribution.
Cubing deviations preserves their signs, allowing positive departures to be distinguished from negative departures.
A skewness between -0.5 and 0.5 indicates an approximately symmetric distribution.
Values beyond positive one or negative one signal substantial asymmetry that violates standard normality assumptions.
Many statistical tests and linear models perform poorly on heavily skewed features, leading to biased predictions.
Analysts often apply logarithmic or square root transformations to compress right-skewed distributions toward symmetry.