Sampling
GCSE Mathematics – Numeracy and 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
 Understand methods of sampling
 Apply stratified sampling techniques
 Apply systematic sampling techniques
 Consider the reliability of conclusions drawn
GCSE Mathematics
Possible learning outcomes
 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
Sample
 Understand proportional relationships
 Effective representative sampling can produce very good estimates of
Population
characteristics of a population. The larger the sample the greater the accuracy,
 Find a fraction of an amount
Random sample
but this should be balanced against the cost and complexity of carrying out the
 Find a percentage of an amount
Systematic sample
sample.
 Round numbers to an appropriate degree of accuracy
Stratified sample
 A random sample is one where every member of the population has an equal
Strata, stratum
chance of selection. If every member of the population is numbered, a random
Group
number generator on a spreadsheet or calculator can be used. If the chance of
Layer
selection can be determined, then random sampling is sometimes referred to as
Sample size
‘probability sampling’.
Proportion, proportional
 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
Hwb: Question 69: Sampling methods
 Explain how the random number generator on a calculator can be
 Some students may think that a systematic sample always starts
Hwb: Question 97: Stratified sampling
used to generate 10 numbers between 1 and 60
with the selection of the first item
Hwb:
Task
2:
Speed
of
Sound.
This
task
explores
problems
with
 What is the same and what is different: stratified sampling,
 Some students may round incorrectly when calculating the size of
drawing conclusions from too small a sample of data, and may be used
systematic sampling?
groups in a stratified sample
as
an
introduction
to
sampling.
 (Given a table of values with 600 in a population, 37 in a particular
 Some students may not appreciate that a larger sample size is likely
group, and a sample size of 50) Ross writes the following calculation Kangaroo Maths: Stratified sampling
to yield more accurate information about the population
50
for working out the size of this group in the sample: 600 × 37. Jenna
37
writes this calculation: 600 × 50. Who is correct? Explain your
answer.