In this paper, we analyze the average age of information (AoI) and the average peak AoI (PAoI) of a multiuser mobile edge computing (MEC) system where a base station (BS) generates and transmits computation-intensive packets to user equipments (UEs). In this MEC system, we focus on three computing schemes: (i) The local computing scheme where all computational tasks are computed by the local server at the UE, (ii) The edge computing scheme where all computational tasks are computed by the edge server at the BS, and (iii) The partial computing scheme where computational tasks are partially allocated at the edge server and the rest are computed by the local server. Considering exponentially distributed transmission time and computation time and adopting the first come first serve (FCFS) queuing policy, we derive closed-form expressions for the average AoI and average PAoI. To address the complexity of the average AoI expression, we derive simple upper and lower bounds on the average AoI, which allow us to explicitly examine the dependence of the optimal offloading decision on the MEC system parameters. Aided by simulation results, we verify our analysis and illustrate the impact of system parameters on the AoI performance.