I intuitively understand the examples below, but I don't see an "average" in the average rate of change (I see a ratio of two delta values). What is the relationship between the average (arithmetic mean) and the average rate of change?
2+3+4 / 3 = 3 (arithmetic mean)
4 miles - 2 miles / 2 hours - 1 hour = 2 miles per hour (average rate of change)
The average is the total divided by the count. The average rate of change is the total distance traveled divided by the amount of time. When you take calculus you will see that average rate over an interval is different from instantaneous rate at a point in time.