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Recent studies on out-of-distribution (OOD) detection focus on designing models or scoring functions that can effectively distinguish between unseen OOD data and in-distribution (ID) data. In this paper, we propose a simple yet novel ap- proach to OOD detection by leveraging the phenomenon that the average of feature vector elements from convolutional neural network (CNN) is typically larger for ID data than for OOD data. Specifically, the average of feature vector elements is used as part of the scoring function to further separate OOD data from ID data. We also provide mathematical analysis to explain this phenomenon. Experimental evaluations demonstrate that, when combined with a strong baseline, our method can achieve state-of-the-art performance on several OOD detection benchmarks. Furthermore, our method can be easily integrated into various CNN architectures and requires less computation. Source code address: https://github.com/SYSU-MIA-GROUP/statistical_discrepancy_ood.