﻿ Unit 18 Section 2 : Sampling Techniques

# Unit 18 Section 2 : Sampling Techniques

In this section we look at two further techniques for sampling: systematic sampling and quota sampling.

A systematic sample is taken by sampling at regular intervals.

A quota sample is when the different categories that make up the population are represented according to their proportion within the overall population.

A typical use of quota sampling is in opinion poll surveys where there is a need to reflect the way the population breaks down between the two genders, into different age groupings, into cultural and ethnic backgrounds, etc. The choice of people selected from each category is left to the person collecting the information.

We will use the class from Example 1 at the beginning of this unit to demonstrate how to use these sampling techniques. The names are listed again below:

 1 Alan 10 Rachel 19 Sacha 28 Salif 2 Lucy 11 Ben 20 Halim 29 Annie 3 Tom 12 Emma 21 Daniella 30 Karen 4 Azar 13 Hannah 22 Joseph 5 Jayne 14 Grace 23 Anna 6 Nadima 15 Miles 24 Sophie 7 Matthew 16 James 25 Kathryn 8 Sushi 17 Joshua 26 Helen 9 Mohammed 18 Lisa 27 Fatoumata

## Example 1

Select a systematic sample of size

(a)

5,

As there are 30 pupils in the class, and we want a sample of 6, we calculate 30 ÷ 6 = 5. We can then obtain our sample of size 6 by selecting every 5th member of the class.

This would give:

 5 Jayne 10 Rachel 15 Miles 20 Halim 25 Kathryn 30 Karen
(b)

6 from the class.

For a sample of size 5 we could select every 6th member of the class:

 6 Nadima 12 Emma 18 Lisa 24 Sophie 30 Karen

You can select a systematic sample of size 6 by choosing any of the first 5 items as a starting point and then taking every 5th item thereafter. For example, in part (a) we could have started with pupil number 2 (Lucy) and then selected pupils number 7, 12, 17, 22 and 27. This would have generated the sample

Lucy, Matthew, Emma, Joshua, Joseph, Fatoumata.

Similarly, starting with pupil number 4 (Azar) in part (b) would have generated the sample

Azar, Rachel, James, Joseph, Salif.

## Example 2

Create a quota sample of size 10 from the class.

Note that the class contains 12 boys and 18 girls.

As the ratio of boys to girls is 2 to 3 in the class, they must be in the same ratio in the sample.
So for a sample of 10 we need 4 boys and 6 girls. These do not need to be chosen at random, and so could be:

 Alan Lucy Tom Jayne Azar Nadima Matthew Sushi Rachel Emma

If the teacher is selecting the pupils then it is possible that they may choose their favourite 4 boys and 6 girls, which would introduce some bias to the sample. It is best to avoid this possibility by selecting 4 boys randomly from the group of 12 boys, likewise for the girls. This produces a stratified random sample. We will look at stratified random samples in more detail in section 18.3

## Exercises

Question 1

Select a systematic sample of size 10 from the class used in Example 1. The first name is written in for you.

Tom

Question 2

There are 400 trees in a plantation. All the trees have been planted in rows.
Create a systematic sample of 24 trees.

16

Question 3

The houses in a street are numbered from 1 to 340.
Create a systematic sample of size 20.

17

Question 4

A theatre group has 40 members of whom 15 are boys. A quota of size 8 is to be interviewed. How many girls and how many boys should be included in the sample?

girls and boys
Question 5

Is a quota sample also a random sample?

Quota samples are not random.
The different samples (from which the quotas are selected) are usually of different sizes, so not every member of the population has an equal chance of being selected. Even if the categories were all equal in size, we would still not get a random sample because the person conducting the survey decides who to choose (usually based on simple convenience).
Question 6

Is a systematic sample a random sample?

A systematic sample is not random because the items in the sample are determined immediately the starting point has been decided.
Question 7

A company employs the following numbers of staff in 3 categories:

 Management 10 Technical 20 Administrative 20

How many from each category should be included in a quota sample of size:

(a)

10

(b)

5

(c)

25?

Question 8

Refer to the members of the computer club in question 7 of Exercise 18.1.
Create systematic samples of size:

 Dee 12 Max 16 Ollie 18 Denise 14 Nazir 15 James 11 Tom 16 Jane 17 Hannah 14 Holly 11 Ferdi 11 Gemma 13 Richard 15 Kim 14 Nadia 16 Jai 13 Grant 12 Hugh 14 Victor 13 Juliette 13 Ben 13 Peter 14 Nigel 14 Ali 15
(a)

8,

(b)

6,

(c)

4 from the list of members

Question 9

In a street the homes numbered 1 to 70 are houses and those numbered 71 to 90 are bungalows.

(a)

Which home numbers would you include in a systematic sample of size 18 ?

(b)

How many bungalows would you include in a quota sample of size 18 ?

bungalows
(c)

Comment on the number of bungalows included in each sample.

systematic sample:
quota sample:
Question 10

For the homes described in question 9, use the following random number table to create a random sample of size 18.

3 2 3 7 9 9 0 4 2 4 0 9 4 2 8 6 5 9 8 1 0 9 9 2 8 8 1 5 1 6 5 6 2 0 8 2 0 7 2 6 1 4 2 6 0 3 9 1 9 7
7 5 2 7 2 0 6 1 1 3 2 8 1 0 1 0 5 9 0 8 5 2 8 6 8 3 3 9 3 0 0 0 6 7 2 5 5 0 0 5 7 4 8 4 1 9 1 8 4 1

Number of bungalows included in this sample =

This time all the 3 samples include the same number of bungalows.