# Deriving the standard error of the mean formula

I don't understand , here $X$ is data like for ex. height in a class :

$X_1=186cm$

$X_2=186.9cm$

$X_3=188cm$

and so on ... or they are independent random vars like one var for height other for weight and so on ?

The first step is confusing for me , please explain the following :

The variance of $T=(X_1+X_2+X_3 + ... X_n)$ is $n\sigma^2$

Why ?

The variance of the sum of independent random variables is the sum of their variances. So if $X_1$, $X_2$... all have variance $\sigma^2$ then the sum is $n\sigma^2$.
• so the $X_i$ here are all random vars, it confused me because the article says observations .... so I thought that they meant observations for a particular random var. – Oleg Mar 22 '17 at 0:24