GCSE Mathematics – Numeracy and GCSE Mathematics / GCSE Mathematics
Specifying the problem and planning
- Specifying the data needed and considering potential sampling methods
- Sampling systematically
- Working with stratified sampling techniques and defining a random sample
- Considering the effect of sample size and other factors that affect the reliability of conclusions drawn
Possible learning objectives / Possible learning outcomes
- Understand methods of sampling
- Apply stratified sampling techniques
- Apply systematic sampling techniques
- Consider the reliability of conclusions drawn
- Understand the difference between a sample and a population
- Understand the purpose of sampling
- Choose an appropriate method of sampling
- Know the definition of a random sample
- Use the random number generator on a calculator to generate random numbers
- Know how to take a systematic sample
- Understand when it is appropriate to use a stratified sample
- Understand that the size of each group in a stratified sample is proportional to the size of the group in the population
- Calculate the size of each group in a stratified sample
- Consider the effect of sample size
Prerequisites / Mathematical language / Pedagogical notes
- Understand proportional relationships
- Find a fraction of an amount
- Find a percentage of an amount
- Round numbers to an appropriate degree of accuracy
Population
Random sample
Systematic sample
Stratified sample
Strata, stratum
Group
Layer
Sample size
Proportion, proportional /
- Effective representative sampling can produce very good estimates of characteristics of a population. The larger the sample the greater the accuracy, but this should be balanced against the cost and complexity of carrying out the sample.
- A random sample is one where every member of the population has an equal chance of selection. If every member of the population is numbered, a random number generator on a spreadsheet or calculator can be used. If the chance of selection can be determined, then random sampling is sometimes referred to as ‘probability sampling’.
- A systematic sample takes items from a list at fixed regular intervals. It is most often applied in quality control processes. A systematic sample is not a ‘simple’ random sample. However, if the first item is chosen at random, then systematic sampling is an example of ‘equal probability sampling’.
- A stratified sample is appropriate when there are obvious strata (layers, or groups) within the population. The size of each group in the sample is proportional to the size of each group in the population. A stratified sample can be a random sample. Stratified sampling is more complex, and therefore more expensive.
- WJEC: New content guidance includes worked examination questions and annotated candidates’ responses.
Reasoning opportunities and probing questions / Possible activities / Potential misconceptions
- Explain how the random number generator on a calculator can be used to generate 10 numbers between 1 and 60
- What is the same and what is different: stratified sampling, systematic sampling?
- (Given a table of values with 600 in a population, 37 in a particular group, and a sample size of 50) Ross writes the following calculation for working out the size of this group in the sample: . Jenna writes this calculation: . Who is correct? Explain your answer.
Hwb: Question 97: Stratified sampling
Hwb: Task 2: Speed of Sound. This task explores problems with drawing conclusions from too small a sample of data, and may be used as an introduction to sampling.
Kangaroo Maths: Stratified sampling /
- Some students may think that a systematic sample always starts with the selection of the first item
- Some students may round incorrectly when calculating the size of groups in a stratified sample
- Some students may not appreciate that a larger sample size is likely to yield more accurate information about the population