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Analysis of range queries on spatial (multidimensional) data is both important and challenging. Most previous analysis attempts have made certain simplifying assumptions about the data sets and/or queries to keep the analysis tractable. As a result, they may not be universally applicable. This paper proposes a set of five analysis techniques to estimate the selectivity and number of index nodes accessed in serving a range query. The underlying philosophy behind these techniques is to maintain an auxiliary data structure, called a density file, whose creation is a one-time cost, which can be quickly consulted when the query is given. The schemes differ in what information is kept in the density file, how it is maintained, and how this information is looked up. It is shown that one of the proposed schemes, called cumulative density (CD), gives very accurate results (usually less than 5 percent error) using a diverse suite of point and rectangular data sets, that are uniform or skewed, and a wide range of query window parameters. The estimation takes a constant amount of time, which is typically lower than 1 percent of the time that it would take to execute the query, regardless of data set or query window parameters.