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LearnCambridge97092026–2027Paper 6 · Probability & Statistics 2Sampling and estimation

Paper 6 · Module

Sampling and estimation

3 subtopics≈ 110 min in total

Start the module: Sampling and unbiased estimates Open graphing calculator

Sampling and unbiased estimates
We usually can't measure a whole population, so we measure a random sample and estimate. The sample mean estimates $\mu$ fairly, but for the variance we divide by $n-1$ , not $n$ , to stop the estimate coming out too small on average.
≈ 35 min
The sample mean and the Central Limit Theorem
The mean of a random sample is itself a random variable. It is centred on $\mu$ , its spread shrinks like $\dfrac{\sigma}{\sqrt n}$ , and for large samples it is approximately normal whatever the population looks like.
≈ 35 min
Confidence intervals
A single estimate is almost certainly a little wrong. A confidence interval gives a range, $\bar x\pm z\dfrac{\sigma}{\sqrt n}$ , built so that in, say, $95\%$ of samples the range would capture the true mean.
≈ 40 min