A-Level Mathematics Revision — Statistical Sampling
Revise Statistical Sampling for A-Level Mathematics with a topic explanation, worked example and common mistakes. Check the board notes for specification differences.
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What is Statistical Sampling?
Statistical sampling at A-Level involves selecting a subset of individuals from a larger population to estimate characteristics of the whole population. You will learn about different sampling methods, such as simple random sampling, systematic sampling, and stratified sampling, and understand the concepts of bias and variance.
Board notes: All A-Level Maths boards (AQA, Edexcel, OCR) cover statistical sampling. The emphasis on different sampling methods and the complexity of the problems can vary slightly between boards.
Step-by-step explanationWorked examples
Worked example
A school has 800 students, with 440 boys and 360 girls. A stratified sample of 50 students is required. The number of boys in the sample should be (440/800) * 50 = 27.5, which we round to 28. The number of girls in the sample should be (360/800) * 50 = 22.5, which we round to 22. So the sample should contain 28 boys and 22 girls.
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Common mistakes
- 1Confusing random sampling with haphazard sampling. Random sampling requires a systematic method to ensure every member of the population has an equal chance of being selected.
- 2Not understanding the purpose of stratified sampling. This method is used to ensure that subgroups of a population are represented proportionally in the sample.
- 3Making errors in calculations for systematic sampling, particularly when determining the interval size.
Statistical Sampling exam questions
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Frequently asked questions
What is the difference between a census and a sample?
A census is a survey of the entire population, while a sample is a survey of a subset of the population. A census is more accurate but is often impractical due to time and cost.
What is bias in sampling?
Bias in sampling occurs when the sample is not representative of the population. This can happen if the sampling method is flawed, leading to an over- or under-representation of certain groups.