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CIE A-Level Maths Study Notes

5.4.1 Sample vs. Population

This section focuses on the fundamental concepts of samples and populations in statistics. We will explore the difference between these two concepts, understand the importance of randomness in sample selection, discuss potential biases in non-random sampling methods, and examine the fundamental reasons for randomness in sampling.

What Are Samples and Populations?

  • Population: The entire group you're interested in. Example: All people in the UK.
  • Sample: A smaller group picked from the population for study. Example: 1,000 people from the UK.
Sample and Populations

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Key Points:

  • Scope: Population = everyone in the group. Sample = a part of the population.
  • Feasibility: Studying a population is hard; samples are easier and cheaper.
  • Inference: We study samples to learn about the population.

Why Randomness Matters in Samples

  • Equal Chance: Every member of the population has an equal chance to be in the sample. This reduces bias.
  • Representation: A random sample is more likely to represent the whole population well.

Example Illustration: Random Sampling

Random Sampling

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Biases in Non-Random Sampling

  • Volunteer Bias: People who volunteer might not represent everyone.
  • Self-Selection Bias: People choose themselves, possibly skewing results.

Ensuring Randomness

  • Unbiasedness: Random samples accurately represent the population.
  • Reliability: Random samples give consistent results.

Practical Example: School Survey

  • Objective: Randomly select 120 students from 1,200 for a survey.
  • Method: Assign numbers to all students, and use a random number generator to pick 120 students.

Steps for a Random Sample Selection

  • List Population: Number each student 1 to 1,200.
  • Random Selection: Use a program to pick 120 unique numbers.
  • Survey: Conduct the survey with the chosen students.
Dr Rahil Sachak-Patwa avatar
Written by: Dr Rahil Sachak-Patwa
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Oxford University - PhD Mathematics

Rahil spent ten years working as private tutor, teaching students for GCSEs, A-Levels, and university admissions. During his PhD he published papers on modelling infectious disease epidemics and was a tutor to undergraduate and masters students for mathematics courses.

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