Transcript slides

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?