Post on 04-Jan-2016
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© Nuffield Foundation 2011
Nuffield Free-Standing Mathematics Activity
Parking permits
Student parkingParking 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.
Types of data
Qualitative or Quantitative
ContinuousDiscrete
Primary or 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:
• selected by a random process
• representative
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 samplingThink about…How might this be done?
Total15 542
Student population of college
19+16–18
5465871L1
30011247L2
11761097L3
2118567
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
14122
7732
3028
5515
Think about…What percentage are in each category?
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.
0.2813994148
0.9035005852
0.5192867333
0.0923297718
Examples Random sample from group of 871 students
281
903 too large – discard
519
92
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
Other considerations
• cost
• time
• response rate
• convenience
Think about…What else should you bear in mind?
• 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?
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?