Deep learning methods nowadays rely on massive data, resulting in substantial costs of data storage and model training. Data selection is a useful tool to alleviate such costs, where a coreset of massive data is extracted to practically perform on par with full data. Based on carefully-designed score criteria, existing methods first count the score of each data point and then select the data points whose scores lie in a certain range to construct a coreset. These methods work well in their respective preconceived scenarios but are not robust to the change of scenarios, since the optimal range of scores varies as the scenario changes. The issue limits the application of these methods, because realistic scenarios often mismatch preconceived ones, and it is inconvenient or unfeasible to tune the criteria and methods accordingly. In this paper, to address the issue, a concept of the moderate coreset is discussed. Specifically, given any score criterion of data selection, different scenarios prefer data points with scores in different intervals. As the score median is a proxy of the score distribution in statistics, the data points with scores close to the score median can be seen as a proxy of full data and generalize different scenarios, which are used to construct the moderate coreset. As a proof-of-concept, a universal method that inherits the moderate coreset and uses the distance of a data point to its class center as the score criterion, is proposed to meet complex realistic scenarios. Extensive experiments confirm the advance of our method over prior state-of-the-art methods, leading to a strong baseline for future research. The implementation is available at https://github.com/tmllab/Moderate-DS.