Venstreskjev

Venstreskjev, also called left-skewness or negative skew, describes a probability distribution with a longer left tail than the right tail. In such distributions, most observations cluster toward higher values, while a minority extend toward lower values. Consequently, the order of measures of central tendency tends to be mean < median < mode (when defined): the mean is pulled downward by the left tail, the median lies between, and the mode is typically at or near the peak on the right.

Identification: A histogram or density plot shows a longer tail to the left. The skewness coefficient, such as the Fisher-Pearson moment coefficient gamma1, is negative for left-skew. Outliers on the lower end can contribute to the left tail; sample estimates may be unstable for small samples.

Examples: An easy exam can yield a left-skewed score distribution, with many students scoring high and a few very low scores. Some quality-control measurements with a natural lower bound may also appear left-skewed.

Implications: Skewness affects the interpretation of the mean as a measure of central tendency and can influence statistical methods that assume normality. When appropriate, the median or nonparametric tests are more robust for skewed data. Transformations for left-skew data often involve reflecting the data (multiplying by −1) before applying a typical normalization, or applying nonparametric methods.