# A Mathematically Sensible Explanation of the Concept of Statistical Population

## TL;DR

This paper introduces a new mathematically rigorous framework for understanding the concept of statistical population and sampling, aiming to clarify a traditionally vague topic in statistics education.

## Contribution

It provides a clear definition of population and explores the relationship between simple random sampling and iid variables within a new theoretical framework.

## Key findings

- Defined population with mathematical precision
- Analyzed the relationship between simple random sampling and iid variables
- Enhanced understanding of statistical population concept

## Abstract

In statistics education, the concept of population is widely felt hard to grasp, as a result of vague explanations in textbooks. Some textbook authors therefore chose not to mention it. This paper offers a new explanation by proposing a new theoretical framework of population and sampling, which aims to achieve high mathematical sensibleness. In the explanation, the term population is given clear definition, and the relationship between simple random sampling and iid random variables are examined mathematically.