# Why is it necessary to assume that a sample vector consists of n sample variables instead of assuming that we have a sample of size n?

This is a very basic question, but I need help to grasp the concept. From what I understand:

1. If I carry out a survey on body weight, every single answer to the question "How much do you weigh?" is a sample variable.

2. Several sample variables form the sample vector.

3. The sample function (e.g. mean) assigns such a sample vector a real number.

4. The advantage of assuming that each observation is a sample variable is that the value which results from the application of the sample function is also a random variable, which permits the application of (axioms of) probability theory.

My question is this: Why is it not possible to apply probability theory based on the following:

• Q1. A single sample of 30 observations is drawn. These 30 observations form the sample variable (vis-a-vis 1. and 2, this would be the pendant to the sample vector.).
• Q2. Given that the 30 observations were drawn randomly, the sample function is also a random variable, which permits the application of (axioms of) probability theory.

Furthermore, is it not - again conceptually - "dishonest" to claim that there exist millions of sample variables, each of a particular body weight, instead of recognizing that "body weight" is a variable, of which these sample variables are really just particular realizations?

Am I making an issue of a non-issue?

Thank you!

• So this question has been answered here: link. But perhaps someone could explain this using the above scenario (body weight) as an example to make it clearer in the concrete. – Spaniel19 Jan 4 at 9:29