Average speed is defined by the following formula
here
D = total distance that an object move from its initial position to final position
t = total time of the motion
so here we will say that there is no such relation between initial or final speed or we can say maximum or minimum speed of object with average speed of object.
We only need to find the total distance and total time of motion in order to find the average speed
here we can see many examples like let say an object moves with speed v1 for time t1 and then with speed v2 for time t2 then here average speed is given as
since we know that distance covered is product of speed and time
that's why we used above equation for finding total distance
now the average speed will be
so this is how we can find the average speed for above motion
so average speed is always between maximum and minimum speed any value in-between.
It is neither the maximum value nor it is minimum value