1. © Nuffield Foundation 2011 Nuffield Free-Standing Mathematics Activity Parking permits

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

3. Types of data Qualitative or Quantitative Continuous Discrete 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: selected by a random process representative

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

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

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. 0.2813994148 0.9035005852 0.5192867333 0.0923297718 Examples Random sample from group of 871 students 281 903 too large – discard 519 92

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

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

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

11. Reflect on your work Parking permits 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?