Modern artificial intelligence (AI) applications require large quantities of training and test data. This need creates critical challenges not only concerning the availability of such data, but also regarding its quality. For example, incomplete, erroneous, or inappropriate training data can lead to unreliable models that produce ultimately poor decisions. Trustworthy AI applications require high-quality training and test data along many quality dimensions, such as accuracy, completeness, and consistency. We explore empirically the relationship between six data quality dimensions and the performance of 19 popular machine learning algorithms covering the tasks of classification, regression, and clustering, with the goal of explaining their performance in terms of data quality. Our experiments distinguish three scenarios based on the AI pipeline steps that were fed with polluted data: polluted training data, test data, or both. We conclude the paper with an extensive discussion of our observations.