Relative Mean Difference

Definition

The mean absolute difference between all pairs of values in a dataset, divided by the arithmetic mean. It is a scale-free measure of dispersion and is directly related to the Gini coefficient.

Why It Matters

Unlike the standard deviation, the relative mean difference is scale-free and therefore suitable for comparing variability across datasets measured in different units or at different magnitudes. Its direct connection to the Gini coefficient makes it particularly useful in inequality research, where a normalised dispersion measure is needed to compare income distributions across countries or time periods.

Example

Two countries have average incomes of $25,000 and $50,000, but their relative mean differences are 0.38 and 0.52 respectively. Despite the second country's higher absolute income, its relative inequality is greater, indicating a wider gap between rich and poor relative to the mean.

Related Terms

• Gini Coefficient
• Mean (Arithmetic)
• Coefficient of Variation (CV)

Software Notes

• SPSS: Not built-in; compute via Transform > Compute Variable with mean absolute difference formula
• R: mean(abs(outer(x, x, "-"))) / mean(x) or use ineq package for Gini-related measures
• Stata: ineqdec0 variable from the ineqdeco package; relative mean difference equals 2 x Gini