Age of Information (AoI), defined as the time elapsed since the generation of the latest received update, is a promising performance metric to measure data freshness for real-time status monitoring. In many applications, status information needs to be extracted through computing, which can be processed at an edge server enabled by mobile edge computing (MEC). In this paper, we aim to minimize the average AoI within a given deadline by jointly scheduling the transmissions and computations of a series of update packets with deterministic transmission and computing times. The main analytical results are summarized as follows. Firstly, the minimum deadline to guarantee the successful transmission and computing of all packets is given. Secondly, a \emph{no-wait computing} policy which intuitively attains the minimum AoI is introduced, and the feasibility condition of the policy is derived. Finally, a closed-form optimal scheduling policy is obtained on the condition that the deadline exceeds a certain threshold. The behavior of the optimal transmission and computing policy is illustrated by numerical results with different values of the deadline, which validates the analytical results.