Recent work in data integration has shown the importance of statistical information about the coverage and overlap of sources for efficient query processing. Despite this recognition there are no effective approaches for learning the needed statistics. In this paper we present StatMiner, a system for estimating the coverage and overlap statistics while keeping the needed statistics tightly under control. StatMiner uses a hierarchical classification of the queries, and threshold based variants of familiar data mining techniques to dynamically decide the level of resolution at which to learn the statistics. We will demonstrate the major functionalities of StatMiner and the effectiveness of the learned statistics in BibFinder, a publicly available computer science bibliography mediator we developed. The sources that BibFinder integrates are autonomous and can have uncontrolled coverage and overlap. An important focus in BibFinder was thus to mine coverage and overlap statistics about these sources and to exploit them to improve query processing.