1. A computer implemented 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 having a data value from a plurality of possible data values with a probability characterized by a respective individual probability distribution function, 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 probability distribution function 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 probability distribution function and a first plurality of individual probability distribution functions characterizing the first subset of the plurality of ordered data items, wherein the method further comprises: electronically determining a plurality of representative value errors based on a distance metric, the plurality of representative value errors corresponding to a respective plurality of possible representative data ranges and respective possible representative probabilities; electronically determining a plurality of representative probability distribution function errors based on the plurality of representative value errors, the plurality of representative probability distribution function errors corresponding to a respective plurality of possible representative probability distribution functions associated with a respective plurality of possible buckets, each possible bucket bounded by a respective possible beginning data item and a respective possible ending data item; and electronically partitioning the plurality of ordered data items into the plurality of buckets and electronically determining the first representative probability distribution function based on the plurality of representative probability distribution function errors, the respective plurality of possible representative probability distribution functions, and the respective plurality of possible buckets, the plurality of buckets being selected from the plurality of possible buckets, the first representative probability distribution function being selected from the plurality of possible representative probability distribution functions.