  Income inequality measures are often used as an indication of economic
health. How to obtain reliable confidence intervals for these measures based on
sampled data has been studied extensively in recent years. To preserve
confidentiality, income data is often made available in summary form only (i.e.
histograms, frequencies between quintiles, etc.). In this paper, we show that
good coverage can be achieved for bootstrap and Wald-type intervals for
quantile-based measures when only grouped (binned) data are available. These
coverages are typically superior to those that we have been able to achieve for
intervals for popular measures such as the Gini index in this grouped data
setting. To facilitate the bootstrapping, we use the Generalized Lambda
Distribution and also a linear interpolation approximation method to
approximate the underlying density. The latter is possible when groups means
are available. We also apply our methods to real data sets.
