I am doing the single variable calculus lecture from the MIT OpenCourseWare, in one lecture when they were teaching about the numerical integrations—more specifically, the Simpson's rule. In the lecture, they gave a formula for the average height (or weighted average height) of a parabola: $\frac{Y_0 + 4Y_1 + Y_2}{6}$). I didn't understand the formula "very well"; when I googled it, I found a post on the stack that was asking the same question—I guess he didn't understand that lecture very well as well. But the proof given in the post went straight over my head, but I found a video on the Simpson's formula by Eddie Woo; it cleared the derivation part. Still, I am confused by the formula, and what it is signifying.
How can the middle of height—so to say—be more weighted than the others, what is that 4 signifying in the formula? I am not able to understand that.
PS, I don't how to add equations using LaTex.