In this paper, we consider a point-to-point wireless communication system. The source monitors a physical process and generates status update packets according to a Poisson process. The packets are transmitted to the destination by using finite blocklength coding to update the status (e.g., temperature, speed, position) of the monitored process. In some applications, such as real-time monitoring and tracking, the timeliness of the status updates is critical since the users are interested in the latest condition of the process. The timeliness of the status updates can be reflected by a recently proposed metric, termed the age of information (AoI). We focus on the packet management policies for the considered system. Specifically, the preemption and discard of status updates are important to decrease the AoI. For example, it is meaningless to transmit stale status updates when a new status update is generated. We propose three packet management schemes in the transmission between the source and the destination, namely non-preemption (NP), preemption (PR) and retransmission (RT) schemes. We derive closed-form expressions of the average AoI for the proposed three schemes. Based on the derived analytical expressions of the average AoI, we further minimize the average AoI by optimizing the packet blocklength for each status update. Simulation results are provided to validate our theoretical analysis, which further show that the proposed schemes can outperform each other for different system setups, and the proposed schemes considerably outperform the existing ones without packet management at medium to high generation rate.