Comparison of Income Inequality Using Ratios of the Mean to the Median as a Disparity Coefficient

Mean and median values are widely used metrics to characterize various populations, but full attention has not been paid to the meaning of differences in these two measures. We hypothesized that the ratio of the mean (m) to the median (M) (m/M) could be useful to detect different patterns of distribution in a population. Analyzing household income of the United States, we found strong correlations between the m/M ratio and the Gini coefficient over the past 30 years (R2 : 0.9472). The Gini coefficient is predicted to be 0.37m/M. A similar tendency was observed in Japan over the same period. Furthermore, there is a strong correlation between these parameters and disposable incomes for 31 Organization for Economic Co-operation and Development (OECD) and 4 non-OECD nations. Especially for the top half of countries in the Gini coefficient, the correlation is very strong (R2 : 0.9797 and is predicted to be 0.4m/ M-0.13.) Taken together, the m/M ratio may serve as an alternative index to detect social disparities when Gini coefficient is not available. The parameter may be also useful to measure deviations in distributions within populations in other fields of economics and science.