The observed increase in economic inequality, where the major concern is relative to the huge growth of the highest incomes, motivates to revisit classical measures of inequality and to offer new ways to synthesize the variability of the entire income distribution. The idea is to provide policy makers a way to contrast the economic position of the group of the poorer "p" percent of the population and to compare their mean income to the one owned by the "p" percent of the richest. The new measure is still a Lorenz-based one, but the significant focus is based here in equally sized and opposite parts of the population whose difference is so remarkable nowadays. We then highlight the specific information given by the new inequality measure and curve, by comparing it to the widely employed Lorenz curve and Gini index and the more recent Zenga approach, and provide an application to Italian data on household income, wealth, and consumption along the years 1980-2012. The effects of estimating inequality indices and curves from grouped data are also discussed.