Sampling

Question 1

What is a population?

Answer 1

A FULL collection of people or things. They can be finite or infinite.

Question 2

What is a sample?

Answer 2

A subset of the population that intends to represent the population.

Question 3

What is a census?

Answer 3

When data is obtained from ALL members of the population.

The entire population is used.

Question 4

What is a sampling frame?

Answer 4

The list of all those in the population that can be sampled.

Question 5

What is a sampling unit?

Answer 5

Each individual thing in the population that can be sampled.

Question 6

What are the strengths and weaknesses of using a census?

Answer 6

+ Should give completely accurate results - representative.

• Time consuming and expensive.
• Can not be used when testing involves destroying the sampling units.
• Large volume of data to process.

Question 7

What are the strengths and weaknesses of using a sample?

Answer 7

+ Cheaper
+ Quicker
+ Less data to process

• Data may not be accurate.
• Data may not be large enough to represent small sub-groups.

Question 8

What would you usually write when a question asks to…

Suggest one way that they could improve their estimate?

Answer 8

Use a larger sample size.

Question 9

What is simple random sampling and how would you carry it out?

There are 64 girls and 56 boys in a school. Explain briefly how you could take a random sample of 15 pupils using a simple random sample. [3 marks]

Answer 9

Every sample has an equal chance of being selected.

= METHOD =

1) Allocate a number between 1 and N (total number of sampling frame) to each pupil.

2) Use a random number generator to select 15 DIFFERENT numbers between 1 and 120.

3) Pupils corresponding to these numbers become the sample.

Question 10

What are the strengths and weaknesses of using simple random sampling?

Answer 10

+ Bias free
+ Easy and cheap to do
+ Each no. has an equal chance of being selected.

• Not suitable when population size is large.
• Sampling frame is needed.

Question 11

What is systematic sampling and how would you carry it out?

A telephone directory contains 50,000 names. A researcher wishes to select a systematic sample of 100 names from the directory. Explain in detail how the researcher should obtain such a sample. [2 marks]

Answer 11

Sampling units are chosen at regular intervals in an ordered list.

= METHOD =

1) Randomly select a number between 001 and 500 using a random number generator.

2) Then select every 500th person from that number.

i.e. Take every kᵗʰ element where…
k = pop size (N) / samp size (n)

The starting point is a random item between 1 and k.
So…
50,000 / 100 = 500
k = 500

Question 12

What are the strengths and weaknesses of using simple random sampling?

Answer 12

+ Simple and quick to use.
+ Suitable for large samples/populations.

• Sampling frame is needed.
• Can introduce bias if sampling frame is not random.

Question 13

What is cluster sampling and how would you carry it out?

A company wants to research the views of A-Level students in the UK to find out what type of revision guides would be most helpful.
Describe how the company might carry out a random cluster sample of 1000 students. [3 marks]

Answer 13

When the population is very large and can be split into many groups.

A random sample of groups is taken and then random samples are taken within each of the groups.

= METHOD =

1) Create a list of schools in the UK and number them.

2) Use a random number generator to select 10 schools from the list that have a corresponding number allocated.

3) Carry out a further random sample of 100 students from each school chosen.

Question 14

What are the strengths and weaknesses of using cluster sampling?

Answer 14

+ Suitable for large samples/populations.
+ Can make things much easier if the population is very large (whole sampling frame isn’t needed. only those of chosen clusters)

• Sampling frames needed.
• Can introduce bias if clusters are too similar.

Question 15

What is quota sampling and how is it carried out?

A lake contains 3 species of fish. There are estimated to be 1400 trout, 600 bass and 450 pike in the lake. A survey of the health of the fish in the lake is carried out and a sample of 30 fish is chosen.

Explain ow this sampling method could be used to select the sample of 30 fish. You must show your working. [4 marks]

Answer 15

Population is divided into groups according to characteristic.

= METHOD =

1) A quota of items/people in each group is set to try and reflect the group’s proportion in the whole population.

2) Interviewer selects the actual sampling units.

Trout =
(1400 / 2450) x 30 = 17.14 (1 mark)

Bass =
(600 / 2450) x 30 = 7.35 (1 mark)

Pike =
(450 / 2450) x 30 = 5.51 (1 mark)

Fish are caught from the lake until the quota of 17 trout, 6 bass and 6 pike are reached.

If a fish is caught and the species quota is full, then this is ignored. (1 mark)

Question 16

What are the strengths and weaknesses of using quota sampling?

Answer 16

+ Allows small sample to still be representative of pop.
+ No sampling frame needed.
+ Quick, easy, cheap.
+ Allows for easy comparison between different groups in population.

• Non-random sampling can introduce bias.
• Population must be divided into groups, which can be costly or inaccurate.

Question 17

What is opportunity/convenience sampling and how would you carry it out?

Answer 17

Sample taken from people who are available at time of study, who meet criteria.

Question 18

What are the strengths and weaknesses of using opportunity/convenience sampling?

Answer 18

+ Easy to carry out.
+ Inexpensive.

• Unlikely to provide a representative sample.
• Highly dependent on individual researcher - bias as they may go during a specific time of day, or choose specific people (outside fish & chip shop on Friday afternoon)