The outlying property detection problem (OPDP) is the problem of discovering the properties distinguishing a given object, known in advance to be an outlier in a database, from the other database objects. This problem has been recently analyzed focusing on categorical attributes only. However, numerical attributes are very relevant and widely used in databases. Therefore, in this paper, we analyze the OPDP within a context where also numerical attributes are taken into account, which represents a relevant case left open in the literature. As major contributions, we present an efficient parameter-free algorithm to compute the measure of object exceptionality we introduce, and propose a unified framework for mining exceptional properties in the presence of both categorical and numerical attributes.