In mediated database systems and in data warehouse systems, there is a single schema used when providing the integrated view of the data. In such systems that have n different data source schemas, at most n different schema mappings must be devised and implemented.
In data warehouse systems, the schema mapping can generally be one-way. The mapping just needs to figure out how to present information in the data source in a way that's consistent with the integrated view's schema.
In mediated systems, the schema mapping must be two-way. Like with a data warehouse, a mapping from the data source schema to the integrated schema must be defined. However, mediated systems receive queries from their users, which must then be translated into queries processed by the data sources. The user formulates the query using terms from the integrated schema. The query posed to the data source by the mediator must be in terms of the data source's schema.