"Summary data" is a representation of "groups of facts." Statistics are a typical example of summary data, which is often a major component of databases that deal with huge domains, such as objects in a whole country or events that occurred over a long time range. Although any summary can be reproduced from the corresponding originals, these are often unavailable and the required data may or may not be derivable from the given summary data. A schema of summary data is defined as a relationship between classifications of object types and domains for attributes. Reclassification rules are introduced as semantic relations among classifications. Set theoretical lemmata provide an inference mechanism that judges derivability of required summary data from collected summary data, and derives the former, if it is derivable, from the latter. It is also shown how this inference mechanism improves a summary database in usability and logical data independence. Discussions are made with examples in the statistical field.