---
tag: 656Y8FA3RY
kind: concept
name: Sampling distribution
msc: ["62E15", 62A01]
specializes: [0DVDCMA2DK]
sources:
  - url: https://en.wikipedia.org/wiki/Sampling_distribution
same_as:
  wikidata: Q3773214
  wikipedia: Sampling distribution
---

## Summary

The sampling distribution of a [[statistic|0Q5CG2NEQ8]] is its probability distribution when the data are random.
It describes how the statistic would vary if the sampling were repeated many times.
Standard errors, confidence intervals and p-values of [[frequentist inference|YDSNHKM3EG]] are all computed from sampling distributions.

## Explanations

### L1 human

Take a sample of $50$ people and compute their average height.
Another sample of $50$ people would give a slightly different average.
The sampling distribution is the pattern of all these averages over all possible samples.
For averages it is centred at the true mean, and its spread shrinks like $1/\sqrt{n}$ as the sample size $n$ grows.