Mr Kidman's Classroom
Revise the key ideas
Populations, samples and data types
- A population is the complete group being studied. A sample is a smaller group selected to investigate it. A census measures every member, which can be costly or impractical.
- Discrete numerical data are counted, such as numbers of siblings. Continuous numerical data are measured, such as height. Categorical data describe groups, such as a travel method.
- A sample should represent the population relevant to the question. Asking only one friendship group about a whole school's preferences risks bias.
- Random sampling gives each population member an equal chance in a simple random selection. Use a complete sampling frame (a list of all population members) and random numbers; avoid duplicate selections if sampling without replacement.
- Systematic sampling takes every kth member after a random start. Check that a repeating pattern in the list does not bias the chosen sample.
For every fifth member, randomly choose a start from positions 1 to 5. If the start is 3, select positions 3, 8, 13 and so on.
- Questionnaires should use clear wording and non-overlapping response categories that cover possible answers. Avoid leading questions such as “Don't you agree that…?”.
Evaluating evidence
- A larger representative sample usually reduces random sampling variation, but size alone cannot remove selection bias. Ten thousand volunteers may still be unrepresentative.
Random sampling variation means chance differences between samples. Selection bias occurs when the selection method consistently favours or leaves out parts of the population.
- Non-response can bias results if people who respond differ from those who do not. State the population, sample size, method and missing responses when interpreting a survey.
- Use statistics to describe distributions rather than claiming every individual has the average value. A mean of 2.4 siblings is possible even though no one has 2.4 siblings.
- Compare both a measure of centre (a typical value) and spread (variation), with context. A higher mean journey time and larger range suggest longer journeys on average and more variation.
Higher — proportional stratified sampling
- Stratified sampling separates a population into groups, then samples in proportion to each group's size. Randomly select within each group to avoid bias.
A proportional stratified sample - Worked example: A school has 120 Year 10 and 180 Year 11 students. For a proportional sample of 50, choose 50 × = 20 from Year 10 and 30 from Year 11.
- For non-integer group allocations, round carefully so the sample total still matches the target. Explain how any remaining places are assigned.
- Stratification improves representation of the chosen groups; it does not guarantee every relevant characteristic is represented or that answers are unbiased.
Higher — Stratified sampling
- Allocate whole people — Three strata (population groups) contain 41, 59 and 100 people, giving a population of 200. For a sample of 13, exact proportional allocations are 2.665, 3.835 and 6.5. One justified rounding approach takes the whole-number parts 2, 3 and 6, then assigns the two remaining places to the largest fractional remainders: 0.835 and 0.665. The final allocation is 3, 4 and 6. Explain the chosen rule and randomly select within each stratum. Rounding every figure upwards would wrongly produce 15 places.
