24.1 Collecting data, sampling and questionnaires — Learn

Prerequisites: fractions, percentages and reading tables.

Objectives: distinguish a population from a sample; compare sampling methods; write neutral questionnaire questions; describe what a sample can and cannot tell you.

Population, sample and data

A population is the whole group a question concerns. A sample is the smaller group measured. Data collected first-hand are primary data; data collected earlier by someone else are secondary data. A sample can suggest patterns in a population, but its limits matter.

Example. A school has 900 pupils. A random sample of 90 pupils includes 27 who walk. Estimate the percentage who walk.

The sample proportion is $27/90=0.3$.

Convert to a percentage: $0.3\times100=30\%$.

So the estimate is 30%. It may differ from the true population percentage because only some pupils were asked.

Choosing a sample and asking questions

A random sample gives each member a chance of selection. A systematic sample selects at regular intervals from a list. A biased sample is likely to over-represent some views or groups. For example, asking only pupils at the bicycle shelter cannot represent every pupil's travel choice.

A questionnaire question should be clear and neutral. “Do you agree that walking is best?” encourages a particular answer. “How do you usually travel to school?” is more neutral. Give answer choices that cover the likely responses, including “other”.

Example. From 60 surveyed pupils, 18 cycle. Estimate the number cycling in a population of 800.

The sample proportion is $18/60=0.3$.

Apply this proportion to the population: $0.3\times800=240$.

The estimate is 240 pupils. This assumes the sample represents the population; it is not an exact count.

Watch out. A large sample can still be biased. Check how people were chosen, not only how many took part.

Progress check

Return to the travel survey. Which pupils would be missing if you asked only people entering by car? Explain why that matters.

You should now be able to

• identify a population and a sample;
• compare random and biased sampling;
• write a neutral questionnaire question;
• use sample proportions to estimate a population and state a limitation.