Glossary

Mean Difference

The mean difference is the arithmetic mean of all pairwise absolute differences between observations. It is a measure of dispersion that gives less weight to extreme deviations compared with the standard deviation.

Definition

Why It Matters

The mean difference provides an intuitive and robust alternative to the standard deviation for measuring spread. Because it averages absolute differences rather than squared differences, it is less influenced by extreme values. This makes it particularly useful for distributions with heavy tails or outliers where the standard deviation may be misleadingly large. The mean difference also has a direct connection to inequality measurement: the relative mean difference (mean difference divided by the mean) is twice the Gini coefficient, providing a bridge between dispersion and inequality analysis.

Example

Consider a small dataset of incomes: 20, 25, 30, 35, and 100 thousand pounds. The standard deviation is heavily influenced by the outlier (100), yielding a value of approximately 30.5. The mean difference, averaging all pairwise absolute differences, gives a more moderate measure of dispersion that is less distorted by the single extreme value. This property makes the mean difference attractive in income distribution studies and other settings where outliers are common but should not dominate the analysis.

Related Terms

Software Notes

SPSS: No built-in function; compute manually using Transform > Compute Variable with pairwise difference calculations, or use the PROXSCAL procedure for distance matrices
R: mean(diff(combn(x, 2))) for mean of absolute pairwise differences; or use mean(abs(outer(x, x, "-"))) for vectorised computation
Stata: No built-in command; compute using mata for pairwise difference matrices or use community-contributed gini packages that report mean difference