Data streams produced by mobile devices, such as smartphones, offer highly valuable sources of information to build ubiquitous services. However, the diversity of embedded sensors and the resulting data deluge makes it impractical to provision such services directly on mobiles, due to their constrained storage capacity, communication bandwidth and processing power. Unfortunately, the improving hardware capabilities of devices are unlikely to resolve these structural issues. We, therefore, believe that mobile data management systems should, instead, handle data streams efficiently and compactly, to provision services directly at the edge, while accounting for the limits of existing assets and network infrastructures. This paper introduces the FLI framework, which leverages a piece-wise linear approximation technique to capture compact representations of data streams in mobile devices. Our experiments, performed on Android and iOS devices, show that FLI outperforms the state of the art both in memory footprint and I/O throughput. Our Flutter implementation of FLI can store stream datasets in mobile devices, which is a prerequisite to processing big data from ubiquitous devices in situ.