rightskew

Right-skew, also called right-skewed or positively skewed, describes a statistical distribution whose tail extends to higher values. In such distributions the bulk of observations lies at the lower end, with a long tail reaching to the right. This contrasts with left-skew (negative skew), where the tail is on the left.

Key properties include a mean that is typically greater than the median, which is greater than the mode, though exact ordering can vary with the shape. The distribution is not symmetric, and its spread is driven by a few unusually large values that pull the mean upward. The skewness of a distribution is captured by the skewness coefficient, a standardized third moment that is positive for right-skew. Pearsonian measures provide simple summaries such as the difference between mean and median relative to the standard deviation.

Common sources and examples of right-skewed data include income distributions, which have many lower earners and a long tail of high incomes; insurance claim sizes; waiting times; and the distribution of certain financial asset prices or time-to-failure data.

Implications for analysis include departures from normality, which can affect parametric tests and confidence intervals. To address skewness, data transformations such as logarithms or Box–Cox transformations are often used to stabilize variance and approximate symmetry. When reporting central tendency, the median is more robust to extreme values than the mean, and the mode indicates the location of the distribution’s peak.

See also: skewness, normal distribution, data transformation.