Average velocity

Symbol $v_{avg}$ or $\bar{v}$, in meters per second. The definition is displacement over elapsed time, $\vec{v}_{avg} = \frac{\Delta \vec{x}}{\Delta t}$, which is how the AP Physics 1 CED states it in EK 1.2.B.2. It is a vector and it points along the displacement, not along the path.

Only the two endpoints enter the calculation. An object at $x = 2.0$ m when $t = 0$ and at $x = 14.0$ m when $t = 4.0$ s has an average velocity of $12.0/4.0 = 3.0$ m/s however erratically it moved in between.

The endpoint average only works under constant acceleration. The shortcut $v_{avg} = \frac{v_{x0} + v_x}{2}$ is a real equation, but it is a consequence of uniform acceleration and not a definition. Take a car that starts at rest and finishes at 20 m/s after 10 s. Accelerate it uniformly and the average velocity is 10 m/s over 100 m. Leave it parked for 9.0 s and then bring it to 20 m/s in the last 1.0 s and it covers 10 m, an average velocity of 1.0 m/s, from an identical pair of endpoint velocities.

On a position-versus-time graph, average velocity is the slope of the straight line joining the two endpoints, while instantaneous velocity is the slope of the tangent. Around any closed path the average velocity is exactly zero.