© 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?