Why does dividing the final(chosen) height in a line by 2 give you the average height(y) in that line?

Question

I was taught, of course, that the average of something is the sum of all the parts divided by the number of those parts.

This is easy when it is a set of values(2, 6, 8) because its simply (2+6+8)/3 = 16/3 ≈ 5.33.

But when you have a line, you have an **infinite amount of values** divided by **infinity**, right?

So how is it even possible to take the average? And why can you simply divide it by 2 when its a line?

And then of course there is the question about the average of curves and whatnot…

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I feel so dumb, plz help me understand.

**Also this question comes from the idea that average velocity is half the final velocity**

In: 0

Answer 1

You’re almost there. You said it: “you have an infinite amount of values divided by infinity”. This is the math concept of Limits (which leads to Calculus, but we don’t need to go there). Simple case for a straight line: 3 points: (0, 1 ,2) /3 =1. Now take more, smaller steps: (0, 0.5, 1.0, 1.5, 2.0)/ 5 = 1. Keep going: (0, 0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0)/9 =1. You are *approaching* the case you said:”an infinite amount of values divided by infinity”. We can see by the pattern, that as the number of points increases (even “to infinity”) the result is still 1. The Limit for this case is 1.