How skewness and kurtosis affect your distribution

Use skewness and kurtosis to help you establish an initial understanding of your data.

Skewness

Skewness is the extent to which the data are not symmetrical. Whether the skewness value is 0, positive, or negative reveals information about the shape of the data.
Figure A
Figure B
Symmetrical or non-skewed distributions

As data becomes more symmetrical, its skewness value approaches zero. Figure A shows normally distributed data, which by definition exhibits relatively little skewness. By drawing a line down the middle of this histogram of normal data it's easy to see that the two sides mirror one another. But lack of skewness alone doesn't imply normality. Figure B shows a distribution where the two sides still mirror one another, though the data is far from normally distributed.

Positive or right skewed distributions

Positive skewed or right skewed data is so named because the "tail" of the distribution points to the right, and because its skewness value will be greater than 0 (or positive). Salary data is often skewed in this manner: many employees in a company make relatively little, while increasingly few people make very high salaries.

Negative or left skewed distributions

Left skewed or negative skewed data is so named because the "tail" of the distribution points to the left, and because it produces a negative skewness value. Failure rate data is often left skewed. Consider light bulbs: very few will burn out right away, the vast majority lasting for quite a long time.

Kurtosis

Kurtosis indicates how the peak and tails of a distribution differ from the normal distribution. Use kurtosis to help you initially understand general characteristics about the distribution of your data.
Baseline: Kurtosis value of 0

Data that follow a normal distribution perfectly have a kurtosis value of 0. Normally distributed data establishes the baseline for kurtosis. Sample kurtosis that significantly deviates from 0 may indicate that the data are not normally distributed.

Positive kurtosis

A distribution with a positive kurtosis value indicates that the distribution has heavier tails and a sharper peak than the normal distribution. For example, data that follow a t distribution have a positive kurtosis value. The solid line shows the normal distribution and the dotted line shows a distribution with a positive kurtosis value.

Negative kurtosis

A distribution with a negative kurtosis value indicates that the distribution has lighter tails and a flatter peak than the normal distribution. For example, data that follow a beta distribution with first and second shape parameters equal to 2 have a negative kurtosis value. The solid line shows the normal distribution and the dotted line shows a distribution with a negative kurtosis value.

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