Sample means
Specialist Mathematics · Unit 4 — Further calculus and statistical inference · Statistical inference
Learning objectives (4)
LO-1Model and solve problems that involve sample means, with and without technology.LO-2Understand the concept of the sample mean 𝑋 as a random variable whose value varies between samples where 𝑋 is a random variable with mean 𝜇 and the standard deviation 𝜎.LO-3Use repeated random sampling data from a variety of distributions and a range of sample sizes to examine properties of the distribution of 𝑋 across samples of a fixed size 𝑛, including its mean 𝜇, its standard deviation 𝜎 √𝑛 (where 𝜇 and 𝜎 are the mean and standard deviation of 𝑋) and its approximate normality if 𝑛 is large.LO-4Use repeated random sampling data from a variety of distributions and a range of sample sizes to examine the approximate standard normality of 𝑋−𝜇 𝑠 √𝑛 for large samples (𝑛 ≥ 30), where 𝑠 is the sample standard deviation (Central limit theorem).
Practise these objectives with instant AI marking
Adaptive questions tied to QCAA mark schemes. Free to start.
Start free practice