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In statistics, we rarely have access to an entire population. Instead, we collect a sample and use it to estimate population parameters. This lesson covers sampling methods, the concept of a sampling distribution, and how to construct confidence intervals.
Studying an entire population is often impractical or impossible:
| Reason | Example |
|---|---|
| Cost | Surveying every household in a country |
| Time | Testing every item from a production line |
| Destructive testing | Crash-testing every car produced |
| Infinite population | All possible measurements of a physical constant |
A well-chosen sample can provide reliable estimates of population parameters.
Every member of the population has a known, non-zero chance of being selected.
| Method | Description |
|---|---|
| Simple random sampling | Every member has an equal chance; often done using random-number generators |
| Stratified sampling | Population divided into strata (groups); random samples drawn from each stratum |
| Cluster sampling | Population divided into clusters (e.g., schools, regions); entire clusters are randomly selected |
| Systematic sampling | Every kth member is selected from a list, starting from a random point |
Not every member has a known chance of selection. Results may not be generalisable.
| Method | Description |
|---|---|
| Convenience sampling | Whoever is easiest to reach |
| Voluntary response | Participants self-select (e.g., online polls) |
| Quota sampling | Non-random selection to match specific proportions |
Warning: Non-probability samples are prone to selection bias and should be used with caution.
The sampling distribution is the probability distribution of a statistic (like the sample mean) computed from many repeated samples of the same size from the same population.
If you draw all possible samples of size n from a population with mean μ and standard deviation σ:
Mean of x̄: μ_x̄ = μ
Standard error of x̄: SE = σ / √n
The standard error (SE) measures how much the sample mean varies from sample to sample. As n increases, SE decreases — larger samples give more precise estimates.
A point estimate is a single number used to estimate a population parameter.
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