If we decide to use a sample for a survey or questionnaire, there are four types of samples we can use.
**Random sample **

In a random sample, every member of the population has an equal chance of being included. For example, when a computer selects a customer at random to be surveyed about a mobile phone company, every customer of that company has an equal chance of being selected.

**Stratified sample **

In a stratified sample, different categories in a population are represented according to the size of each category and then members of each category are selected randomly.

For example, a school's population may be made up of72% junior students and 28% senior students. A stratified sample of school students must also be made up of 72% junior students and 28% senior students.

**Systematic sample **

In a systematic sample, selections are made on a regular basis. For example, testing every 500th battery manufactured to check that the machines producing the batteries are working properly.

**Self-selected sample **

In a self-selected sample, whoever wishes to participate answers the questions asked. For example, when a television show asks people to ring in and answer a Yes/No question, anyone can participate.

### 0

Example 3The United Club has 14 100 members. This table

gives a breakdown of members by age group. _{Less than 30 years }
Andrew is considering four different of ways of 30 to 39 years
choosing a sample of the members for his market 40 to 49 years
research. Which type of sample is each one? 50 years and over
a Every 100th member on the alphabetical membership list

b Names selected randomly by the computer

**Number of members **
2100
2700
5100
4200
c Putting up a sign at the entrance of the club asking members to volunteer

d 21 members less than 30 years old, 27 members 30 to 39 years old, 51 members 40 to 49 years old and 42 members aged 50 years or more.

### Solution

a Selections are made on a regular basis, in this case every 100th member.

b Every member of the population has an equal chance of being included and the computer chooses randomly.

c Any member who volunteers can participate.

Systematic sample Random sample

When we use a stratified sample, we need to calculate how many people from each category should be included in the sample.

### 0 Example 4

Jason decided to use a stratified sample to survey members at his local gym. There are 970 gym members, 590 are female and 380 are male. He plans to survey 10% of the members.

a How many members will Jason survey? b How many female members should he survey? c How many male members should he survey?

### Solution

a Calculate 10% of the membership. 10% of 970 = 10 lO0 X 970

=97

Jason should survey 97 members. 590

- x97=59 970

**b ** Female members make up 590 out of
970 members. Find the fraction of the

number of members surveyed. Jason should survey 59 female members.

c Males are 380 out of 970 members.

OR

380

- X 97=38 970

Calculate the total to be surveyed minus the number of females.

97 members -59 females = 38 males Jason should survey 38 males.

**EXERCISE 2.03 **

_{Types of samples }

_{Types of samples }

ii\,i,,i,,M Which type of sampling is described in each case? a Selecting every 105th name from the phone book.

**b ** The names of all prefects are placed in a hat and 2 are drawn out to represent the school at
a council function.

c A television program asks viewers to respond to a Yes/No question.

**d ** Selecting an appropriate number of students from each year at your local high school.
e Door prizes drawn out of a barrel.

f The audience at a concert finds prize tickets under every 5th seat in each row. g A company sends out an email to customers asking for their opinions.

**h ** Employees are sorted from tallest to shortest and every 5th employee completes a
questionnaire.

20 females and 28 males were surveyed out of a group of athletes with 100 females and 140 males in it.

j A customs officer searching every 10th person walking through customs.

k A medical researcher advertises for people to participate in a health survey. 5 cards are selected from a pack of cards without looking.

m An import/export business employs i25 women and 250 men. 17 women and 34 men are surveyed about their work hours.

2 Children from 400 families attend the local infants/primary school. The P&C has raised money for new play equipment in the playground and wants to interview parents about their ideas. The committee would like to survey 40 families. Suggest how they might select the 40 families using a:

a random sample b stratified sample

c systematic sample d self-selected sample.

3

**HH**_{n}**HII **

Amanda is going to use a stratified sample to survey the parents of her local netball
club. There are 540 children playing netball. There are 380 primary students and 160 high
school students. Amanda is going to survey 15% of parents.
_{n}

a How many parents should complete the survey?

b How many parents of primary students should complete the survey? c How many parents of high school students should complete the survey?

4 Kieran wishes to survey Year 8 students about their opinions of the school. There are 96 boys and 69 girls in Year 8. He aims to survey 20% of students.

a How many students should complete the survey?

b How many boys should complete the survey?

5 Joanna is going to ask a sample of her Facebook friends about their favourite sport. She has 376 single friends and 416 friends in a relationship. She is going to survey 12.5% of her friends. a How many friends will she survey?

b How many single friends will be in the survey?

c How many friends in a relationship will be in the survey?

6 Global Communications employs 750 people, 479 males and 271 females. The company intends to survey 75 employees about their working conditions.

a How many males should be surveyed?

**Roy Morgon **
**Research **

**Gciloxy Research **