This article aims to develop a minimally intrusive system of care and monitoring. Furthermore, the goal is to get a cheap, comfortable and, especially, efficient system which controls the physical activity carried out by the user. For this purpose an innovative approach to physical activity recognition is presented, based on the use of discrete variables which employ data from accelerometer sensors. To this end, an innovative discretization and classification technique to make the recognition process in an efficient way and at low energy cost, is presented in this work based on the χ ² distribution. Entire process is executed on the smartphone, by means of taking the system energy consumption into account, thereby increasing the battery lifetime and minimizing the device recharging frequency.