It is argued that the density function, commonly used in the study of urban spatial structure, is more appropriately described as the ‘marginal density function’. From such a marginal density function, it is possible to derive two types of average density function, each being concerned with a particular aspect of the spatial structure of population. The first type is consistent with the standard approach to the ‘average’ in economic analysis, while the second more completely takes account of the urban context. The two types of average density function are examined for different underlying forms of the marginal density function. Of the two types, the second has a greater applicability than the first in the analysis of urban spatial structure.