We are witnessing the emergence of new big data processing architectures due to the convergence of the Internet of Things (IoTs), edge computing and cloud computing. Existing big data processing architectures are underpinned by the transfer of raw data streams to the cloud computing environment for processing and analysis. This operation is expensive and fails to meet the real-time processing needs of IoT applications. In this article, we present and evaluate a novel big data processing architecture named RedEdge (i.e., data reduction on the edge) that incorporates mechanism to facilitate the processing of big data streams near the source of the data. The RedEdge model leverages mobile IoT-termed mobile edge devices as primary data processing platforms. However, in the case of the unavailability of computational and battery power resources, it offloads data streams in nearer mobile edge devices or to the cloud. We evaluate the RedEdge architecture and the related mechanism within a real-world experiment setting involving 12 mobile users. The experimental evaluation reveals that the RedEdge model has the capability to reduce big data stream by up to 92.86% without compromising energy and memory consumption on mobile edge devices.