Average velocity is equal to ratio of total displacement to total time. Velocity is a vector quantity and average velocity is defined as the total displacement undergone by the body per unit time.

Displacement in first instance $=v_{1}t$

Displacement in second instance $=v_{2}t$

$\therefore$Average velocity $=\frac{v_{1}t+v_{2}t}{t+t}=\frac{v_1+v_2}{2}$