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MathidiaMathematics Academy
Statistical investigation
Lesson 61 of 75
Introduction

Sampling methods

Objective. Identify bias and choose representative sampling methods.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Sampling methods are techniques for selecting a smaller group from a larger population to represent it fairly in a statistical study, avoiding bias that would skew results. A simple random sample gives every member of the population an equal chance of selection, often achieved by numbering the population and using random numbers. A stratified sample divides the population into groups (strata), such as age bands, and selects proportionally from each group so the sample reflects the population's structure. Bias occurs when a sampling method systematically favours certain outcomes, such as surveying only people leaving a gym about exercise habits, which would not represent the wider population.

Worked example

A school has 300 pupils: 180 in Key Stage 3 and 120 in Key Stage 4. A stratified sample of 50 pupils is needed. How many pupils should come from Key Stage 3?

300 … 180
Illustrated card showing 300 … 180
  1. 1Find the proportion of the school in Key Stage 3: 180/300.
  2. 2Simplify the proportion: 180/300 = 3/5.
  3. 3Multiply this proportion by the total sample size: 3/5 × 50.
  4. 43/5 × 50 = 30.

Answer: 30 pupils

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Common mistake. Pupils often pick a sample purely for convenience, such as surveying only their own classmates about a school-wide issue, without recognising this excludes other year groups and introduces bias. Always check whether every relevant group has a fair chance of being included.

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