Sampling distributions of the sample sum and sample mean and the central limit theorem

What this note covers

1. A statistic has a distribution across samples
2. Mean and spread of an independent sample sum
3. The sample mean becomes more concentrated
4. Normal populations give exact normal sums and means
5. The central limit theorem for non-normal populations
6. Random sampling, finite populations and interpretation
7. Choosing between the sample sum and sample mean
8. How sample size controls a rare mean

8 sections · 10 key terms & formulas · 6 common mistakes