D2 Collecting and sampling data Specification coverage • D2.1 inferring properties of populations or distributions from a sample, whilst knowing the limitations of sampling • D2.2 appreciating the strengths and limitations of random, cluster, stratified and quota sampling methods and applying this understanding when designing sampling strategies (appreciating that improving accuracy by removing bias and increasing sample size may cost/save both time and money)
Collins AQA Foundation GCSE maths • Chapter 3, Statistics: Charts, tables and averages • Chapter 18, Statistics: Representation and interpretation
Resources • Internet access to the poll error in 1936 Landon/Roosevelt (see below)
Prior knowledge •
Perhaps students need to be reminded that √n means the square root of n. Otherwise no prior knowledge is needed here: students may well have studied some or all of these terms before in GCSE Mathematics or GCSE Statistics, but full explanations are given in the Student Book to ensure all students have full access to the work.
Learning objectives • •
Deduce properties of populations from a sample, whilst realising the limitations. Appreciate the advantages and disadvantages of various sampling methods.
Key terms and definitions • • • •
•
Bias: a distortion of results. Census: used when every member of the population provides data. Cluster sample: used to collect data from all members of a randomly selected cluster (or group).Population: a complete set of items that share a common property. Quota sample: used to collect data chosen by the sampler from a stratum (or layer) where the number of items selected is proportional to the size of the stratum in the population.Random sample: used to collect data from part of a population without bias. Sample: part of a population. Sampling: used to collect data from part of a population.Stratified sample: used to collect random data from a stratum (or layer) where the number of items selected is proportional to the size of the stratum in the population.
Common misconceptions •
Confusing the words ‘qualitative’ and ‘quantitative’. Remind students that quantities are measured, so they require the use of numbers, and that the word ‘quantitative’ starts the same way as ‘quantities’.
AQA Level 3 Mathematical Studies (Core Maths) 18 Teacher Guide – Chapter 1
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