An upper bound of the Gini index in the absence of mean income information

In this paper, an upper bound of the Gini index, based on grouped data, is proposed assuming that there is no information on all the group mean incomes as well as the overall mean income but the limits of the income brackets are known. An important advantage of this proposal is that conventional formulas for the upper bound of the Gini index could be applied directly by substituting the (unknown) mean income for each income bracket with the corresponding value that maximizes the grouping correction for that income bracket. The effects of varying the number and size of income brackets are investigated.