1. A method to represent data using a probabilistic histogram, the method comprising: electronically partitioning a plurality of ordered data items into a plurality of buckets, each of the data items capable of having a data value from a plurality of possible data values with a probability characterized by a respective individual probability distribution function (PDF), each bucket associated with a respective subset of the plurality of ordered data items bounded by a respective beginning data item and a respective ending data item; and electronically determining a first representative PDF for a first bucket associated with a first subset of the plurality of ordered data items by partitioning the plurality of possible data values into a first plurality of representative data ranges and respective representative probabilities based on an error between the first representative PDF and a first plurality of individual PDFs characterizing the first subset of the plurality of ordered data items.