Statistics › Section G · The central limit theorem › Topic G.1
The central limit theorem for sample means
Draw one sample, get one mean; draw another, get a different one. Statistics vary - and the central limit theorem turns that nuisance into the foundation of all inference: averages are approximately normal, centred on the truth, with a spread that shrinks predictably as samples grow.
In this topic
- Averages have their own behaviour
- Sampling variability
- The sampling distribution
- Centre and spread: the standard error
- The central limit theorem
- Worked example: clinic waiting times
- Worked example: bottle fills
- Bias and variability
- Why this chapter matters
- Common mistakes to avoid
- Key takeaways
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