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This paper introduces an empirical approach to dispatch resources in real-time power system operation with growing levels of uncertainties emerging from intermittent and distributed energy resources in the supply and the demand side. It is shown that by taking empirical data of specific sizes, the dispatch results can lead to a quantifiable and rigorous bound on the risk of violating constraints at the implementation stage. In particular, we formulate the look-ahead real-time economic dispatch problem using the scenario approach. This approach takes empirical data as input and guarantees a tunable probability of violating the constraints according to the input data size. By exploiting the structure of the economic dispatch, we show that in the absence of transmission constraints, the number of samples theory requires does not grow with the size of the problem. In the more general case with consideration of transmission constraints, it is shown that the posterior bound on the risk of dispatch can be quantified and can be much smaller than the risk bound before solving the dispatch. Numerical examples based on a standard test system suggest that the scenario approach can provide a practically attractive solution with theoretically rigorous properties for risk-limiting power system operations.