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Statistical Sampling — A-Level Mathematics Revision

Revise Statistical Sampling for A-Level Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel and OCR.

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Statistical Sampling in A-Level Mathematics: explanation, examples, and practice links on this page.
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Practice is aligned to major specifications (AQA, Edexcel, OCR, WJEC, Eduqas, Cambridge International (CIE), SQA, IB, AP).
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Related topics in Statistics

  • Probability
  • Statistical Distributions
  • Normal Distribution
  • Statistical Hypothesis Testing

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 explanation

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

Exam-style questions for Statistical Sampling with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel and OCR specifications.

Statistical Sampling exam questions

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Practice QuestionQ1
2 marks

A student is working through a Statistical Sampling problem. Solve the following and show your full working.

A) 12x + 4
B) 4(3x + 1)
C) 12x − 4
D) 3x + 4

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Step-by-step method

Step-by-step explanation

4 steps · Worked method for Statistical Sampling

1

Core concept

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…

3 more steps below
2

Worked method

Apply the key method step-by-step, showing all your working clearly.

3

Common pitfalls

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4

Exam technique

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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.

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