The paper introduces a family of approximate schemes that extend the process of computing sample mean in importance sampling from the conventional OR space to the AND/OR search space for graphical models. All the sample means are defined on the same set of samples and trade time with variance. At one end is the AND/OR sample tree mean which has the same time complexity as the conventional OR sample tree mean but has lower variance. At the other end is the AND/OR sample graph mean which requires more time to compute but has the lowest variance. The paper provides theoretical analysis as well as empirical evaluation demonstrating that the AND/OR sample tree and graph means are far closer to the true mean than the OR sample tree mean.