Nuffield Free-Standing Mathematics Activity Parking permits

1. Nuffield Free-Standing Mathematics Activity Parking permits

2. Student parking Parking at college is a problem. A permit system might help. The principal wants to collect a representative sample of views from students. Think about…How might this be done?

3. Continuous Discrete Types of data Qualitative or Quantitative Primary or Secondary Think about…Can you suggest some examples?

4. Populations and samples A census involves the whole population. A sample involves just part of the population. To avoid bias, a sample should be: • representative • selected by a random process

5. A representative sample reflects the population in the proportion that have relevant characteristics. Think about…How might this be done? Stratified sampling Decide what characteristics are relevant. gender age ethnicity income level Find out how many of the population are in each sub-group (stratum). Divide the sample in the same proportion. Use random sampling to select individuals from each sub-group.

6. Student population of college L1 L2 L3 Other Total15 542 16–18 871 1247 1097 567 19+ 5465 3001 1176 2118 L1 L2 L3 Other 16–18 5.60% 8.02% 7.06% 3.65% 19+ 35.16% 19.31% 7.57% 13.63% L1 L2 L3 Other 16–18 19+ Think about…What percentage are in each category? Representative sample of 400 students Think about…How many should be from each category? 22 32 28 15 141 77 30 55

7. A sample is random if each member of the population has an equal chance of being included. Random numbers Use your calculator to give random numbers. Random sample Examples from group of 871 students 0.2813994148 281 too large – discard 0.9035005852 903 0.5192867333 519 92 0.0923297718

8. Designing a questionnaire Think about…What should you bear in mind? Questions should be: • short , simple, and easy to understand • easy to answer Avoid: • ambiguity • leading questions • personal or embarrassing questions Also consider how to analyse the results

9. Other considerations Think about…What else should you bear in mind? • cost • time • convenience • response rate

10. Common survey methods • postal Think about…What methods can you suggest? • market researcher • telephone • internet • newspaper or magazine Think about…Will these methods give a representative sample?

11. Parking permits • Reflect on your work What is meant by a representative sample? What are the main steps in selecting a stratified sample? What must you bear in mind when designing a questionnaire? List three different ways of collecting views from the general public. What are their advantages and disadvantages?