Like for the derivation of the standard error although i understand in when i look at it but in my mind theres this other scenario playing like why cant it be like var((x1+x2+x3+x4+x5)/5)=var(5x/5) though it doesnt make sense since on the first one youll get the SE= (sigma)/sqrt(5) on the other hand what will be left on var(5x/5)= just var(x) which will be just SE = sigma. I know its wrong but i feel im having difficulty finding the second one as not true because i might be missing or have not learned a fundamental principle.

Comments and feedbacks will be highly appreciated. Thanks in advance