Originated from distributed learning, federated learning enables privacy-preserved collaboration on a new abstracted level by sharing the model parameters only. While the current research mainly focuses on optimizing learning algorithms and minimizing communication overhead left by distributed learning, there is still a considerable gap when it comes to the real implementation on mobile devices. In this paper, we start with an empirical experiment to demonstrate computation heterogeneity is a more pronounced bottleneck than communication on the current generation of battery-powered mobile devices, and the existing methods are haunted by mobile stragglers. Further, non-identically distributed data across the mobile users makes the selection of participants critical to the accuracy and convergence. To tackle the computational and statistical heterogeneity, we utilize data as a tuning knob and propose two efficient polynomial-time algorithms to schedule different workloads on various mobile devices, when data is identically or non-identically distributed. For identically distributed data, we combine partitioning and linear bottleneck assignment to achieve near-optimal training time without accuracy loss. For non-identically distributed data, we convert it into an average cost minimization problem and propose a greedy algorithm to find a reasonable balance between computation time and accuracy. We also establish an offline profiler to quantify the runtime behavior of different devices, which serves as the input to the scheduling algorithms. We conduct extensive experiments on a mobile testbed with two datasets and up to 20 devices. Compared with the common benchmarks, the proposed algorithms achieve 2-100x speedup epoch-wise, 2-7% accuracy gain and boost the convergence rate by more than 100% on CIFAR10.