Various extended relational data models were proposed to handle uncertain data including possibilistic and probabilistic data. Query processing involving aggregate functions over uncertain data is rarely considered. In this paper, we define a set of extended aggregate functions over probabilistic data. The time complexity of the computations for these extended aggregate functions is, in general, exponential. We develop two efficient algorithms for the computation of the maximum and minimum aggregate functions. The worst-case time complexity of the algorithms are O(n2). These algorithms can be extended to handle the possibilistic data. That is, our work is devoted to the accommodation of uncertain data in database systems with an elaboration on speeding up the processing efficiency of the aggregate functions.