Intuition: Average vs. Average Rate of Change

Question

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)

score 1 · Answer 1 · answered Jul 13 '15 at 16:07

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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.

answered Jul 13 '15 at 16:07

John McGee

1,223

Thanks. Are you saying there's no relationship? – mellow-yellow Jul 13 '15 at 16:14
@mellow-yellow that's not at all what he said. – Jul 13 '15 at 17:33
I appreciate everyone's input, but please refer back to my original question: how do the two averages compare to each other, specifically in their shared terminology of "average." – mellow-yellow Jul 13 '15 at 21:42

Intuition: Average vs. Average Rate of Change

1 Answers1