SL 4.1—Sampling and data

A population is the full group a question concerns; a sample is the subset actually observed. Data may be qualitative or quantitative, discrete or continuous, and the type determines which summaries and graphs make sense.

Sampling method changes the route by which evidence enters the study. A random or stratified sample can reduce selection bias, while an opportunity sample is faster but may overrepresent whoever is available and willing.

If 40 of 200 sampled students prefer option A, the 20% is a sample proportion—not a fact about every student. Its usefulness depends on how the 200 were selected and whether the measurements were reliable.

A large sample does not repair a biased selection process. State the target population, sampling frame and likely source of error before generalising.

Sampling map: simple random gives every member an equal selection chance; systematic uses every $k$th member after a random start; stratified samples each subgroup in population proportion; quota fills category targets non-randomly; convenience uses readily available participants. Audit missing values and recording errors before analysis. An outlier lies more than $1.5\times IQR$ below $Q_1$ or above $Q_3$; investigate it rather than deleting it automatically.