Standardization facilitates the management of Internet of Things (IoT) and expedites the generation of IoT big data. However, there is not yet a big data management architecture matching such IoT. Current methodologies, which mainly adopts Simple Network Management Protocol (SNMP), is defective in the following two aspects. First, facing ubiquitous sensor and actuator nodes, timeliness and scalability can hardly be assured by the centralized paradigm. Second, existing management infrastructure cannot perform data analysis and is thus not smart enough, which wastes the value of big data. To address these issues, we propose a big data management architecture for standardized IoT. First, we design a scalable and smart SNMP, which has a hierarchical and decentralized paradigm, and is embedded with edge MapReduce to perform distributed big data analysis. Second, we put forward an Edge MapReduce-based Random Matrix Model (RMM) algorithm for anomaly detection in IoT, which is parallelized and particularly suitable for high-dimensional big data. Third, we conduct a case study of smart grids, where the architecture is implemented using virtual machines and deployed to detect malfunctions in electrical grids. Experiment results demonstrate that the architecture has good performance in terms of timeliness and scalability.