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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.

MethodDescriptionKey Advantage
Simple randomEvery member equally likelyNo bias in selection
StratifiedPopulation divided into groups; proportional sample from eachRepresents all subgroups
SystematicEvery $k$th member from an ordered listQuick 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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