The paper provides a rigorous and exact formulation of the relationship between the Gini measure of inequality in total income across families, and corresponding measures of inequality in such components of total income as wages, transfer income, etc. It is shown that serious problems of bias arise when individual family data are not available and when data on averages for families grouped by the size of total income are used instead. These problems are illustrated with reference to data for Taiwan, 1964 to 1976.