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In fast OLAP applications it is often advantageous to provide approximate answers to range queries in order to achieve very high performances. A possible solution is to inquire summary data rather than the original ones and to perform suitable interpolations. Approximate answers become mandatory in situations where only aggregate data are available. This paper studies the problem of estimating range queries (namely, sum and count) over aggregate data using a probabilistic approach for computing expected value and variance of the answers. The novelty of this approach is the exploitation of possible integrity constraints about the presence of elements in the range that are known to be null or nonnull. Closed formulas for all results are provided, and some interesting applications for query estimations on histograms are discussed.