Some recent accounts of human face processing use the idea of ''face space'', considered to be a multi-dimensional space whose dimensions correspond to ways in which faces can vary. Within this space, ''typicality'' is sometimes taken to reflect the proximity of a face to its local neighbours. Intuitions about the distribution of faces within the space may suggest that the majority of faces will be ''typical'' in these terms. However, when typicality measures are taken, researchers very rarely find that faces cluster at the ''typical'' end of the scale. In this short note we attempt to resolve this paradox and point out that reasoning about high dimensional distributions requires that some specific assumptions are made explicit.