The exponential growth of Internet of Things (IoT) data has pushed the boundaries of data analysis, but it has also raised concerns about the increasing commoditization of personal privacy. The intriguing problem of trading private IoT data is the focal point of this paper. We delve into three fundamental questions: Firstly, we determine the minimum privacy that a broker must purchase from data owners to achieve aggregate statistics with a fixed accuracy goal. Secondly, we propose an innovative arbitrage-free pricing framework that empowers brokers to set prices for aggregate statistics, maximizing utility while ensuring fairness. Lastly, we address the challenge of fairly compensating data owners for their privacy losses while providing economic guarantees. To achieve these objectives, we propose a data trading framework in this paper. Our framework considers ubiquitous data correlations and the potential involvement of untrusted brokers, ensuring that the total compensations remain within the brokers’ budget; each owner is guaranteed to receive non-negative revenues, and cunning data owners cannot exploit misreported privacy demands to gain extra compensations. Experiments on the MovieLens dataset demonstrated the robustness of our framework.