  We first review the derivation of the exact expression for the average
distance $<r_n>$ of the n-th neighbour of a reference point among a set of N
random points distributed uniformly in a unit volume of a D-dimensional
geometric space. Next we propose a `mean-field\rq theory of $<r_n>$ and compare
it with the exact result. The result of the `mean-field\rq theory is found to
agree with the exact expression only in the limit $D \to \infty$ and $n \to
\infty$. Thus the `mean-field\rq approximation is useless in this context.
