The age of data (AoD) is identified as one of the most novel and important metrics to measure the quality of big data analytics for Internet-of-Things (IoT) applications. Meanwhile, mobile edge computing (MEC) is envisioned as an enabling technology to minimize the AoD of IoT applications by processing the data in edge servers close to IoT devices. In this paper, we study the AoD minimization problem for IoT big data processing in MEC networks. We first propose an exact solution for the problem by formulating it as an Integer Linear Program (ILP). We then propose an efficient heuristic for the offline AoD minimization problem. We also devise an approximation algorithm with a provable approximation ratio for a special case of the problem, by leveraging the parametric rounding technique. We thirdly develop an online learning algorithm with a bounded regret for the online AoD minimization problem under dynamic arrivals of IoT requests and uncertain network delay assumptions, by adopting the Multi-Armed Bandit (MAB) technique. We finally evaluate the performance of the proposed algorithms by extensive simulations and implementations in a real test-bed. Results show that the proposed algorithms outperform existing approaches by reducing the AoD around 10%.