High data quality is essential for the performance of many AI systems, especially when techniques involving the training of models are used, with a view to ensure that the high-risk AI system performs as intended and safely and it does not become the source of discrimination prohibited by Union law. High quality training, validation and testing data sets require the implementation of appropriate data governance and management practices. Training, validation and testing data sets should be sufficiently relevant, representative and have the appropriate statistical properties, including as regards the persons or groups of persons on which the high-risk AI system is intended to be used. These datasets should also be as free of errors and complete as possible in view of the intended purpose of the AI system, taking into account, in a proportionate manner, technical feasibility and state of the art, the availability of data and the implementation of appropriate risk management measures so that possible shortcomings of the datasets are duly addressed. The requirement for the datasets to be complete and free of errors should not affect the use of privacy-preserving techniques in the context of the the development and testing of AI systems. Training, validation and testing data sets should take into account, to the extent required by their intended purpose, the features, characteristics or elements that are particular to the specific geographical, behavioural or functional setting or context within which the AI system is intended to be used. In order to protect the right of others from the discrimination that might result from the bias in AI systems, the providers should be able to process also special categories of personal data, as a matter of substantial public interest within the meaning of Article 9(2)(g) of Regulation (EU) 2016/679 and Article 10(2)g) of Regulation (EU) 2018/1725, in order to ensure the bias monitoring, detection and correction in relation to high-risk AI systems.