This paper presents findings on mitigating the negative impact of renewable energy resources variability on the energy scheduling problem, in particular for island grids and microgrids. The methods and findings presented in this paper are twofold. First, data obtained from the City of Summerside in the province of Prince Edward Island, Canada, is leveraged to demonstrate the effectiveness of state-of-the-art time series predictors in mitigating energy scheduling inaccuracy. Second, the outcome of the time series prediction analysis is used to propose a novel data-driven battery energy storage system (BESS) sizing study for energy scheduling purposes. The proposed probabilistic method accounts for intra-interval variations of generation and demand, thus mitigating the trade-off between time resolution of the problem formulation and the solution accuracy. In addition, as part of the sizing study, a BESS management strategy is proposed to minimize energy scheduling inaccuracies, and is then used to obtain the optimal BESS size. Finally, the paper presents quantitative analyses of the impact of both the energy predictors and the BESS on the supplied energy cost using the actual data of the Summerside Electric grid. The paper reveals the significant potential for reducing energy cost in renewable-penetrated grids and microgrids through state-of-the-art predictors combined with applications of properly-sized energy storage systems.