Health-monitoring sensors generate tremendous sensor data, which consumes significant storage memory space and transmission power. To address this pressing need, this work proposes new feature-driven approximation (MFDApx) mechanisms that exploit the feature of sensor data from the application viewpoint to select a proper precision and a reasonable sampling frequency for the heterogeneous sensors that coexisted in a health-monitoring system. The experimental results based on a public MotionSense database show that the proposed MFDApx can reduce the data size by about 50% while maintaining the same accuracy of activity recognition. More interestingly, this work examines the impact of proposed approximation mechanisms on privacy preservation. The simulation results show that downsampling-based approximation can achieve nearly the same accuracy and also reduce the privacy leakage by 12%.