A population is the entire group being studied. A sample is a smaller group selected from the population to represent it.

Why sample? Surveying an entire population is often impractical, expensive, or time-consuming. A well-chosen sample gives reliable conclusions about the population.

Properties of a good sample:

• Representative — reflects the population's characteristics
• Large enough — reduces the effect of chance variation
• Random — every member has an equal chance of being selected

Types of sampling:

• Simple random: every member equally likely to be chosen (e.g. names from a hat)
• Stratified: population split into groups (strata); each group sampled in proportion $$\text{Sample from stratum} = \frac{\text{stratum size}}{\text{population size}} \times \text{sample size}$$
• Systematic: every $n$th member selected from an ordered list

Bias: a sample is biased if certain groups are over- or under-represented, making conclusions unreliable.

Common error: assuming a large sample is automatically unbiased — size doesn't eliminate biased selection.