A method for constructing a histogram can include sampling attributes in a column of a database on a server and determining a bucket set for the histogram based on a number of buckets that represents a distribution of the attributes with minimum error. A bucket in the bucket set includes boundaries and an approximation of a count of attributes falling within the boundaries. The method further includes determining a precision for encoding the approximation, such that the histogram having the bucket set fits within a storage limit on a tangible computer-readable medium. The histogram can then be stored for the database on a tangible computer-readable medium by encoding the approximation with the precision.