Provided are techniques for generating order statistics and error bounds. For each of multiple, distributed data sources, a finite number of data bins are created for each field in that data source. Data values in each of the multiple, distributed data sources are processed to generate basic summaries for each of the data bins in a single pass of the data values. The data bins from each of the multiple, distributed data sources are sorted. One or more approximate order statistics are computed for a data set by accumulating counts from a number of the sorted data bins. Lower and upper error bounds are provided for each of the computed one or more approximate order statistics, wherein the lower and upper error bounds are values delimiting an interval containing a true value of an order statistic.