Sampling and the Central Limit Theorem
How samples behave, and why averages become predictable.
Sampling methods, sampling bias, sampling distributions, standard error, the law of large numbers, the central limit theorem, finite populations and sample size — explored with a sampling simulator.
Lessons
- 1Sampling methodsDescribe simple random, stratified, cluster and systematic sampling, carry each one out, and choose the design that fits a situation.30 minFree
- 2Sampling bias and nonresponseRecognise coverage, nonresponse and voluntary-response bias, quantify how nonresponse distorts an estimate, and correct a survey mean by weighting.30 minMembers
- 3Sampling distributionsExplain what a sampling distribution is, build one from all possible samples, and describe its centre and spread.30 minMembers
- 4Standard errorCalculate the standard error of a sample mean and of a sample proportion, and explain how it differs from the standard deviation.25 minMembers
- 5The law of large numbersState the law of large numbers, use it to explain why averages stabilise, and distinguish it from the gambler's fallacy.25 minMembers
- 6The central limit theoremState the central limit theorem precisely, use it to compute probabilities about a sample mean, and judge how large n must be for a given population shape.35 minMembers
- 7Finite populationsApply the finite population correction to the standard error when sampling without replacement, and decide when it matters.25 minMembers
- 8Sample size, precision and costPlan the sample size needed for a target margin of error, explain the diminishing returns of larger samples, and allow for nonresponse.30 minMembers