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Nuffield Free-Standing Mathematics Activity Parking permits © Nuffield Foundation 2011 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? Types of data Qualitative or Quantitative Discrete Primary or Continuous Secondary Think about… Can you suggest some examples? 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 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. age gender 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. Student population of college 16–18 19+ L1 871 5465 L2 1247 3001 L3 1097 1176 Other 567 2118 L1 L2 L3 Other 16–18 5.60% 8.02% 7.06% 3.65% 19+ 35.16% 19.31% 7.57% 13.63% Total 15 542 Think about… What percentage are in each category? Representative sample of 400 students 16–18 19+ L1 22 141 L2 32 77 L3 28 30 Other 15 55 Think about… How many should be from each category? 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. Examples Random sample from group of 871 students 0.2813994148 281 0.9035005852 903 too large – discard 0.5192867333 519 0.0923297718 92 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 Other considerations Think about… What else should you bear in mind? • cost • time • convenience • response rate Common survey methods • postal • market researcher Think about… What methods can you suggest? • telephone • internet • newspaper or magazine Think about… Will these methods give a representative sample? 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?