The definition of the 'family' by the Australian Bureau of Statistics (ABS) takes the nuclear family as a starting point. Using an anthropological approach to kinship, this paper argues that the nuclear family structure is not a 'natural' outcome of Aboriginal Australian kinship systems, and explores the implications of this for the quality of Indigenous household data in the national Census. The purpose of the research as explored in this article is twofold: to evaluate the ABS Indigenous Enumeration Strategy and to assess the quality of the data that were collected. The paper focuses on the responses to the questions designed to elicit information about family and household structure. These data are supplemented by genealogical information that the author collected in the course of independent anthropological fieldwork.