Statistics and Populations

Statistics enables inferences about a population from a sample. Knowing the limitations of this process — and understanding how different statistical measures and diagrams help describe populations — is central to statistical literacy.

Using Statistics to Describe a Population

Population parameters (e.g. mean height, proportion preferring a product) are estimated using sample statistics. The quality of the estimate depends on:

Sample size: larger samples give more reliable estimates (Law of Large Numbers).
Sampling method: random sampling reduces bias; non-random methods may produce systematically skewed results.
Representativeness: the sample must reflect the diversity of the population.

Limitations of Statistics

Statistical averages describe a group, not any individual within it.
Correlation in data does not imply causation.
Poorly designed questions, biased samples and small datasets all reduce reliability.
Data can be selectively presented to support a particular view — always consider the source and methodology.

The Statistical Enquiry Cycle

Plan (define the question, method, sample) → Collect (gather data) → Process (calculate, draw diagrams) → Interpret (draw conclusions, acknowledge limitations) → back to Plan if needed.

Key Takeaways

Population parameters are estimated from sample statistics — always with uncertainty.
Larger, random, representative samples give more reliable estimates.
Statistics describe groups, not individuals — averages do not apply to every member.
Correlation ≠ causation: two variables may be related without one causing the other.
Always consider bias, sample size and methodology when evaluating statistical claims.