Identify types of data (qualitative and quantitative, discrete and continuous); understand populations and samples; use random and stratified sampling; and recognise sources of bias.

What this dot point is asking

OCR reference S1 covers types of data, populations and samples, sampling methods (including random and stratified) and recognising bias. Good data collection underpins every statistical conclusion, so this content tests the reasoning behind a study as much as any calculation. It appears on every tier, with stratified sampling and bias being reliable Higher and AO2 question types, where a clear, justified explanation earns the marks.

Types of data

Data comes in distinct types that determine how it is handled.

So shoe size is discrete (it jumps in steps), while foot length is continuous (it can be any value). Knowing the type matters because continuous data is grouped into class intervals and shown on a histogram, whereas discrete data may be shown on a bar chart. The distinction guides the choice of chart and average.

Populations and samples

A sample stands in for a population that is too large to survey fully.

So to study the heights of all Year $11$ students in a country (the population), you might measure a sample of a few hundred. The sample must reflect the population's variety, or any conclusion drawn from it will be misleading. Larger samples generally give more reliable results.

Random and stratified sampling

The sampling method affects how representative the sample is.

So for a stratified sample of $50$ from a population of $500$, the sampling fraction is $\tfrac{1}{10}$, and a stratum of $80$ people contributes $8$ to the sample. Stratified sampling ensures small groups are not missed and large groups are not over-represented, which a simple random sample might do by chance.

Recognising bias

A biased sample gives misleading conclusions.

A sample is biased if some members of the population are more likely to be chosen than others, so it is not representative. Surveying only gym-goers about exercise over-represents active people; asking only at one time or place can miss whole groups. To reduce bias, sample randomly from the whole target population and make the sample large enough. Explaining precisely why a sample is unrepresentative, not just calling it "unfair", is the AO2 skill OCR rewards.