Random sampling is one of the most widely used means to build synopses of large datasets because random samples can be used for a wide range of analytical tasks. Unfortunately, the quality of the estimates derived from a sample is negatively affected by the presence of "outliers" in the data. In this paper, we show how to circumvent this shortcoming by constructing outlier-aware sample synapses. Our approach extends the well-known outlier indexing scheme to multiple aggregation columns.