Abstract: Federated learning has emerged as a distributed learning paradigm by training at each client and aggregating at a parameter server. System heterogeneity hinders stragglers from responding to the server in time with huge communication costs. Although client grouping in federated learning can solve the straggler problem, the stochastic selection strategy in client grouping neglects the impact of data distribution within each group. Besides, current client grouping approaches make clients suffer unfair participation, leading to biased performances for different clients. In order to guarantee the fairness of client participation and mitigate biased local performances, we propose a federated dynamic client selection method based on data representativity (FedSDR). FedSDR clusters clients into groups correlated with their own local computational efficiency. To estimate the significance of client datasets, we design a novel data representativity evaluation scheme based on local data distribution. Furthermore, the two most representative clients in each group are selected to optimize the global model. Finally, the DYNAMIC-SELECT algorithm updates local computational efficiency and data representativity states to regroup clients after periodic average aggregation. Evaluations on real datasets show that FedSDR improves client participation by 27.4%, 37.9%, and 23.3% compared with FedAvg, TiFL, and FedSS, respectively, taking fairness into account in federated learning. In addition, FedSDR surpasses FedAvg, FedGS, and FedMS by 21.32%, 20.4%, and 6.90%, respectively, in local test accuracy variance, balancing the performance bias of the global model across clients.