  How to give an upper bound, especially the smallest upper bound of Gini
coefficient based on grouped data in the absence of income brackets is still a
problem not properly solved. This article provides an upper bound which is easy
to compute, and provides an effective algorithm to calculate the exact value of
the smallest upper bound. As illustrations, the calculation results of bounds
for Gini coefficients of urban and rural China from 2003 to 2008 will be
provided.
