When we perform one experiment we have to measure several quantities and take some number of measurements for each of them. Those quantities can be things like positions, instants of time, and so forth.
The point is that we usually end up with a list of measurements $x_1,\dots,x_n$, being $n$ the number of measurements we made.
The important thing is: each $x_i$ corresponds actually to the same thing being measured. It is just that we measure the same thing several times and write down the values.
Once we have this list of measurements we take means, compute standard deviations and so on.
Now, when I asked this question on the answer it was said that when we make the measurements, each $x_i$ is a random variable and the mean is actually another random variable.
I didn't understand that. In truth, my understanding of random variables is quite limited (all I remember of what I once studied on the topic is that random variables are functions defined in a probability space).
Now, I've always thought that on one experiment there was actually just one random variable $x$ which is a discrete random variable with possible values $x_i$ being the values we measured.
But now I see I was wrong all along and each $x_i$ is a random variable. But still, $x_i$ is a measured value, so it should be a number!
I'm quite confused with all of this. What I want to know is: why in one experiment, when we measure $x_1,\dots,x_n$ values of the same quantity, each $x_i$ is itself a random varaible? What is the correct way to reason about this?