Collaborative mobile edge computing (MEC) has emerged as a promising paradigm to enable low-capability edge nodes to cooperatively execute computation-intensive tasks. However, straggling edge nodes (stragglers) significantly degrade the performance of MEC systems by prolonging computation latency. While coded distributed computing (CDC) as an effective technique is widely adopted to mitigate straggler effects, existing CDC schemes exhibit two critical limitations: (i) They cannot successfully decode the final result unless the number of received results reaches a fixed recovery threshold, which seriously restricts their flexibility; (ii) They suffer from inherent poles in their encoding/decoding functions, leading to decoding inaccuracies and numerical instability in the computational results. To address these limitations, this paper proposes an approximated CDC scheme based on barycentric rational interpolation. The proposed CDC scheme offers several outstanding advantages. Firstly, it can decode the final result leveraging any returned results from workers. Secondly, it supports computations over both finite and real fields while ensuring numerical stability. Thirdly, its encoding/decoding functions are free of poles, which not only enhances approximation accuracy but also achieves flexible accuracy tuning. Fourthly, it integrates a novel BRI-based gradient coding algorithm accelerating the training process while providing robustness against stragglers. Finally, experimental results reveal that the proposed scheme is superior to existing CDC schemes in both waiting time and approximate accuracy.