leftskewed

Left-skewed, or negatively skewed, describes a distribution in which the left tail is longer or fatter than the right tail. The bulk of observations cluster at higher values, with a tail extending toward lower values. In a histogram, the peak tends to appear toward the higher end of the scale, and the skewness statistic is typically negative.

Numerical indicators of left skew include a negative skewness value. A common practical rule is that the mean is pulled toward the left by low values, so the mean is smaller than the median, and the median is smaller than the mode. In many cases, the ordering of central tendency is mode > median > mean. Skewness can be estimated with sample statistics, and Pearson’s second skewness coefficient relates mean and median as a quick check: skewness ≈ 3(mean − median).

Common causes or examples include ceiling effects on measurement scales (where many observations pile up near the upper limit) or data generated by processes with inherently bounded lower values. Left-skewed distributions can arise in educational testing when many scores cluster near the top or in ratings systems with hard lower thresholds.

Implications for analysis and interpretation include preferring the median over the mean as a measure of central tendency, and using nonparametric tests when normality is questionable. Transformations to address left skew often involve reflecting the data (for example, transforming X to −X) to apply standard methods, or applying Box-Cox-type transformations after an appropriate adjustment. Robust statistics can also mitigate the influence of extreme low values.