Conventional database systems process all the data (related to a query) before providing a response. This project develops new query processing methods suitable for the database management systems (DBMS) when they are to respond to estimation, error- constrained and time-constrained queries, or when there is no need or there is not enough time to process all the data related to the query. This approach incorporates sampling and sample size determination mechanisms into DBMS so that, with a given user's requirement (e.g., timing or error constraints), the DBMS can determine an appropriate amount of sample tuples that need to be processed in order to produce acceptable estimations for aggregate relational queries. The goal of this research is to provide efficient methods for DBMS that will be able to effectively support time- and error- constrained environments, and serve for other statistical purposes. Furthermore, these facilities will also provide ordinary users with convenient working environments enabling the users to get statistical information about the database as soon (or as precise) as they wish by specifying the timing constraints, sampling fractions or error constraints. Such statistically enhanced DBMSs will find a wide variety of applications.