We consider an arbitrary family of stochastically ordered distribution functions dependent on parameters from an interval in the real line. We compare distribution functions and moments of random variables with distribution functions being the mixtures of the members of the above stochastically ordered family. In particular, we determine lower and upper bounds on the values of one mixture distribution function under the condition that the other mixture distribution is arbitrarily fixed. We also evaluate the differences between the expectations of mixture variables in various scale units. The results are illustrated by some examples.