---
tag: Y0PTCJBPEA
kind: concept
name: Simple random sample
msc: [62D05]
sources:
  - url: https://en.wikipedia.org/wiki/Simple_random_sample
same_as:
  wikidata: Q1056998
  wikipedia: Simple random sample
---

## Summary

A simple random sample of size $n$ from a finite population is a random subset of $n$ units.
It is chosen so that every subset of size $n$ is equally likely.
It is the basic design of survey sampling, against which other designs are compared.
Under it, the sample mean is an unbiased estimator of the population mean with an explicit variance.

## Explanations

### L1 human

Write the name of every member of the population on a ticket, mix the tickets well, and draw $n$ of them without putting any back.
The people drawn form a simple random sample.
Every person has the same chance to be chosen, and moreover every group of $n$ people has the same chance to be the sample.
For instance, from $4$ people, a sample of $2$ is one of $6$ possible pairs, each with probability $1/6$.