Are the categories used to study the social world and acting on it real or conventional ? An empirical answer to that question is given by an analysis of the debates about the quality of statistics produced by the European National Institues of statistics in the 1990s. Six criteria of quality were then specified: relevance, accuracy, timeliness, accessibility, comparability and coherence. How do statisticians and users of statistics deal with the tension produced by their objects being both real (they exist (...) before their measurement) and conventionally constructed (they are in a way, created by these conventions)? In particular, the technical and sociological distinction between the criteria of relevance and accuracy implies a realistic interpretation, desired by users, but that is nonetheless problematic. (shrink)