  We prove uniform estimates for the expected value of averages of order
statistics of bivariate functions in terms of their largest values by a direct
analysis. As an application, uniform estimates for the expected value of
averages of order statistics of sequences of independent random variables in
terms of Orlicz norms are obtained. In the case where the bivariate functions
are matrices, we provide a "minimal" probability space which allows us to
$C$-embed certain Orlicz spaces $\ell_M^n$ into $\ell_1^{cn^3}$, $c,C>0$ being
absolute constants.
