Data collection, sampling and types of data

Types of data

• Qualitative (categorical) — non-numerical: eye colour, sport, brand.
• Quantitative — numerical: height, score, time.
  • Discrete — only certain values (e.g. number of children: 0, 1, 2, …).
  • Continuous — any value in a range (e.g. height, weight, time).

Choosing the correct chart depends on type: bar charts for categorical/discrete; histograms for continuous grouped data.

Population and sample

• Population — every member of the group of interest.
• Sample — a smaller subset used to make inferences about the population.

A good sample is random, representative and large enough.

Sampling methods

• Simple random — every member has an equal chance. Use random numbers or a random number generator.
• Stratified — population split into groups (strata). Sample size from each stratum proportional to its size: stratum size × (sample size ÷ population size).
• Systematic — pick every kth member after a random start.

Bias

A sample is biased if it does not represent the population fairly. Common causes:

• Asking only friends (convenience sample).
• Asking at a specific time/place (e.g. only people in a library).
• Leading questions or response bias.

Data collection — questionnaires (CCEA reasoning marks)

A good question:

• Has a clear time frame ("How many hours per week").
• Has non-overlapping, exhaustive response boxes (0–4, 5–9, 10–14, 15+ — not 0–5, 5–10).
• Avoids leading wording ("Don't you agree…?").

A typical CCEA mark scheme awards B1 for spotting a flaw and B1 for suggesting an improvement.

Common CCEA exam tip

When given a sampling-method question, write which method and why it is appropriate (e.g. "stratified by year group because each year has a different number of pupils and we want proportional representation").