Single-Peaked preferences play an important role in the social choice literature. In this paper, we provide necessary and sufficient conditions for observed behaviour to be consistent with a mixture model of single-peaked preferences for a given ordering of the alternatives. These conditions can be tested in time polynomial in the number of choice alternatives. In addition, algorithms are provided which identify the underlying ordering of choice alternatives if ordering is unknown. These algorithms also run in polynomial time, providing an efficient test for the mixture model of single-peaked preferences.