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MathidiaMathematics Academy
Statistics and distributions
Lesson 64 of 75
Challenge

Sampling and bias

Objective. Design representative samples and diagnose bias.

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

Learn: the key idea

Sampling and bias concerns choosing a smaller group from a population so that it fairly represents the whole, and recognising when a method skews results. A simple random sample gives every member an equal chance of selection, while stratified sampling ensures proportions from subgroups match the population. For example, surveying only people leaving a gym about fitness habits introduces bias because it excludes non-gym-goers entirely. Good sampling design states a clear sampling frame and a method giving fair, unbiased coverage of the whole population being studied.

Worked example

A school has 300 boys and 200 girls. Using stratified sampling to select a sample of 50 students, find how many girls should be chosen.

300 … 200
Illustrated card showing 300 … 200
  1. 1Total students = 300 + 200 = 500
  2. 2Proportion of girls = 200/500
  3. 3Number of girls in sample = (200/500) × 50
  4. 4Number of girls = 20

Answer: 20

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Common mistake. Students often confuse a large sample size with a representative one; a huge but biased sample, like only online survey respondents, still gives misleading conclusions about the wider population.

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