Let X_1, X_2, \cdots, X_n be independent with a common distribution function F(x) which has a finite mean, and let Z_{n1} \leqq Z_{n2} \leqq \cdots \leqq Z_{nn} be the ordered values X_1, \cdots, X_n. The distribution of the n values EZ_{n1}, \cdots, EZ_{nn} on the real line is studied for large n. In particular, it is shown that as n \rightarrow \infty, the corresponding distribution function converges to F(x) and any moment of that distribution converges to the corresponding moment of F(x) if the latter exists. The distribution of the values Ef(Z_{nm}) for certain functions f(x) is also considered.