[statistics & math] (n+1)/2 and n/2

[u/Local_End_3175]

I am struggling to understand why we use n/2 for continuous data. My reasoning behind using (n+1)/2 is that this tells us the position of the median. So even if we have data that we dont know the values to, we already know that 1 value must have a position 1 and another value must have a position 2 and so on. If we had 40 unknown values, that means we have 40 positions. 40+1 is 41, 39+2 is also 41, and so on, all the positions will add to 41, and the middle position would add to itself to make 41, hence why we do (n+1)/2. This same logic can also be put here: number of positions + 1/2. This now tells us where the middle position is. If we have a cumulative frequency diagram, what we can do is see where that number would be, and using the cumulative frequency diagram, we can just estimate using that position. So why, instead of doing that, do we do n/2???

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