Sampling, unbiased estimates and the distribution of the sample mean
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 5 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- What does a sample tell you?
- Sampling methods
- A stratified sample
Read the transcript of the teaching part
Last time
Before we start: last time, in Probabilities from a pdf, its properties and symmetry, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
What does a sample tell you?
You cannot measure every journey, every battery, every voter. So you measure a sample and use it to say something about the whole population. The skill is knowing how far to trust it. Choose the sample fairly, estimate without bias, and know how the sample mean behaves, and you can put numbers on that trust.
Sampling methods
In a simple random sample every member has an equal chance of selection. In a systematic sample you pick every kth member from a list. In a stratified sample you split the population into groups, then sample each group in proportion to its size. A quota sample fills fixed numbers from each group, but not at random, so it can be biased.
A stratified sample
A school has 240, 180, 120 and 60 students in four years, 600 in all. You want a sample of 150, a quarter of the school. Each year contributes a quarter of its size: 60, 45, 30 and 15. Within each year, choose at random. Then the whole sample is fair and also represents each year.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Distribution of the sample mean · Unbiased estimates of mean and variance.
The whole chapter: Sampling and Estimation.
Chapter 6.4: Sampling and estimation
- Sampling, unbiased estimates and the distribution of the sample mean 7 min
- The Central Limit Theorem and confidence intervals 7 min
Also for A Level Maths 9709 Paper 6
Which topics come up most in A Level Maths 9709 Paper 6 past papers, counted from every paper since 2004.