Skewness

TL;DR

• Measures how asymmetric a distribution is (whether values cluster more to one side of the mean).
• Positive skew: longer right tail; negative skew: longer left tail.
• Skew affects central-tendency choices and statistical analyses — when skewed, the median can better represent the “typical” value than the mean.

Definition

Skewness is a measure of the asymmetry of a distribution. It describes how the values of a variable are distributed around the mean (or expected value) of the variable. A distribution is considered symmetrical if the skewness value is close to zero; a skewness value greater than zero indicates positive skewness, and less than zero indicates negative skewness.

Explanation

A distribution is skewed when its values are not evenly distributed around the mean. Positive skewness (right-skewed) means the distribution has a longer tail on the right side; negative skewness (left-skewed) means a longer tail on the left side. Skewness can be calculated using a statistical formula that takes into account the mean, median, and standard deviation of the distribution.

Skewness matters because it can affect the results of statistical tests and analyses. For example, when a distribution is positively skewed, the mean of the distribution may be higher than the median, so the mean may not accurately represent the majority of values. In such cases, using the median as a measure of central tendency may be more appropriate.

Examples

Positive skewness (right-skewed)

An example of a variable with positive skewness is income. In many countries, the distribution of income is skewed to the right, meaning that there are a few individuals with very high incomes, but most individuals have lower incomes. This results in a longer tail on the right side of the distribution, indicating positive skewness.

Negative skewness (left-skewed)

An example of a variable with negative skewness is lifespan. In many countries, the distribution of lifespan is skewed to the left, meaning that there are a few individuals who live to very old ages, but most individuals have shorter lifespans. This results in a longer tail on the left side of the distribution, indicating negative skewness.

Use cases

• Assessing distribution shape when analyzing a variable.
• Informing choice of central tendency (mean vs median) when summarizing data.
• Considering potential impacts on statistical tests and analyses that assume symmetry.

Notes or pitfalls

• A skewness value close to zero indicates a roughly symmetrical distribution.
• When a distribution is positively skewed, the mean may be higher than the median and so may not represent the majority of values.

Related terms

• Mean
• Median
• Standard deviation
• Distribution
• Symmetry
• Statistical tests