Statistical Sampling (AS Unit 2: Applied Mathematics A) — WJEC A-Level Mathematics
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Statistical Sampling (AS Unit 2: Applied Mathematics A) explained
In statistical theory, a population comprises the entire collection of individuals, objects, or measurements about which information is sought, while a sample is a selected subset of the population.
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A complete enumeration of every population member constitutes a census. Although a census provides completely accurate parameters with zero sampling error, it is frequently unfeasible due to prohibitive costs, excessive time constraints, or the destructive nature of testing (such as testing the breaking strain of cables). Sampling offers a practical, cost-effective alternative, though it introduces sampling variation that must be accounted for during inference.
Your focus
- Distinguish between an entire population and a representative sample in statistical investigations.
- Evaluate the practical advantages and limitations of a census compared to taking a sample.
- Identify real-world scenarios where destructive testing makes a full census impossible.
Statistical Sampling (AS Unit 2: Applied Mathematics A) exam tips
Marking Points
- defining a population as the entire set of items under statistical consideration
- defining a sample as a finite subset chosen from a population
- identifying a practical constraint (such as cost, time, or destructive testing) that necessitates sampling
Examiner Tips
- 💡Define populations precisely with explicit geographical and temporal boundaries.
- 💡Cite destructive testing whenever a question asks why a manufacturer cannot inspect every product.
Common Mistakes
- assuming a census is always preferable without recognising practical drawbacks like destructive testing
- confusing sample statistics (such as x̄ and s) with population parameters (such as μ and σ)