Statistical Inference
Year 11 (IGCSE) 📈 Statistics & Probability Sampling, hypothesis basics, interpreting statistical data.
🔍 Populations and Samples
The population is the entire group being studied. A sample is a smaller subset used to draw conclusions about the whole population.
- Census: Data from the entire population — accurate but expensive and time-consuming.
- Sample survey: Data from a representative subset — quicker and cheaper, with some uncertainty.
A good sample must be random and representative — it should reflect the full diversity of the population.
📊 Sampling Methods
Different methods suit different situations. The choice affects reliability.
| Method | Description | Key Advantage |
|---|---|---|
| Simple random | Every member equally likely | No bias in selection |
| Stratified | Population divided into groups; proportional sample from each | Represents all subgroups |
| Systematic | Every $k$th member from an ordered list | Quick and easy |
⚡ Stratified Sample Size
$$\text{Sample from group} = \frac{\text{group size}}{\text{population size}} \times \text{total sample size}$$📈 Making Inferences
Use sample statistics to estimate population parameters, while acknowledging uncertainty from sampling variability.
Example: A random sample of 60 students gives mean height 168 cm. We estimate the population mean is approximately 168 cm — but sampling variability means the true mean could differ.
Larger samples give more reliable estimates. Always check whether the sample may be biased before drawing conclusions about the population.
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