In this paper, we consider the design of a wireless sensor network (WSN) that aims at monitoring the environment and collecting data periodically. In view of the limited energy and computational capability of the sensor nodes, a mobile edge computing (MEC) server is deployed in the WSN as a data processing unit. The goal of the design is to maintain the freshness of the data, which is characterized by the criterion of the age of information (AoI). Therefore, we analyze the long-term average AoI of the considered network. Then, the energy and time constraints for the WSN are modeled with consideration of transmission and computation. Next, a non-convex average AoI minimization problem is formulated subject to the energy and time constraints by jointly optimizing the sampling rate, computing scheduling, and transmit power. To tackle the challenging problem, the geometric programming and successive convex approximation (SCA) technique are applied to develop an algorithm with convergence guarantee. Moreover, to exhibit the benefits of the MEC server, a joint design is investigated for the WSN without the MEC server. Finally, the numerical results demonstrate the efficiency of our proposed SCA-based algorithm and show the impact of the sampling rate on the AoI performance.