In machine learning, the performance of a classifier depends on both the classifier model and the dataset. For a specific neural network classifier, the training process varies with the training set used; some training data make training accuracy fast converged to high values, while some data may lead to slowly converged to lower accuracy. To quantify this phenomenon, we created the Distance-based Separability Index (DSI), which is independent of the classifier model, to measure the separability of datasets. In this paper, we consider the situation where different classes of data are mixed together in the same distribution is most difficult for classifiers to separate, and we show that the DSI can indicate whether data belonging to different classes have similar distributions. When comparing our proposed approach with several existing separability/complexity measures using synthetic and real datasets, the results show the DSI is an effective separability measure. We also discussed possible applications of the DSI in the fields of data science, machine learning, and deep learning.