S1 - finding the lower quartile question, I have the answer, just don't get something

First let me say that the method Edexcel want you to use is completely whacko and sometimes you won't actually get the same answer as you would by finding the median first then going half way to that from the minimum value. But just do it the way they want you to You don't have to but it makes the numbers easier.

For continuous or grouped data only:
$\mathrm{Q}_1 = \frac{n}{4}^\mathrm{\ th\ }\mathrm{value}$
$\mathrm{Q}_2 = \frac{2n}{4}^\mathrm{\ th\ }\mathrm{value}$
$\mathrm{Q}_3 = \frac{3n}{4}^\mathrm{\ th\ }\mathrm{value}$
Where $n$ is the number of pieces of data. Then just find the value with interpolation.

For discrete data only, do the same process as above and then:
If you get an integer (eg. 11^th value) go half way between it and the next value (eg. 11.5^th value).
If you don't get an integer (eg. 13.5th value) you must round up (!) to the next integer (eg. 14^th value) even if you would not normally round up. (eg. 17.25^th value -> 18^th value). Hold up your five fingers. The median finger is the third right? (not the 2.5^th)

Just follow those rules and you'll get the right answer. Totally strange right? But that's what the text book says. If something's not clear, do say.

Wow, holy crap, thank you so much! You answered my question as simply as possible and covered it all.

Where you talked about continuous data in terms of like n/4 for the Q1, is there a way to talk about discrete data in terms of an expression?
So for discrete data:

After following the process for continuous or grouped data, can you talk about it in terms of like (n+1)/4? ie, if you had 100 data pieces and wanted the first quartile, instead of getting 100/4=25 and then half way to 26th term afterwards, can you talk about it as something such as (100+1)/4 and then round it up because it's a decimal?

Am I just over complicating this? I am trying to think of expressions for doing the discrete data, so you add 1 to n then divide by, say 4 for the first quartile, 2 for the second quartile, etc. Am I just over complicating this and over thinking it way too much?

If I am, please tell me that it's pointless what I am trying to work out and I should just use the method you said. I completely understand what you said to me, I think I am just overcomplicating it for no reason with what I am trying to do. If this is the case, let me know please - I overthink the simple stuff way too much in maths and it gets me so confused when I don't need to be.