1.1 Population and samples

Question 1

What does population mean in statistics?

Answer 1

Whole set of items that are of interest

Question 2

Examples of populations

Answer 2

• Items manufactured by a factory
• All the people in town

Question 3

What can be obtained from a population?

Answer 3

Information

Question 4

What is raw data?

Answer 4

Unprocessed information

Question 5

What is a census?

Answer 5

Observes or measures every member of a population

Question 6

What is a sample?

Answer 6

Selection of observations taken from a subset of the population which is used to find out information about the population as a whole

Question 7

What is the advantage of using a census?

Answer 7

It should give a completely accurate result

Question 8

Disadvantages of using a census

Answer 8

1. Time-consuming and expensive
2. Cannot be used when testing process destroys the item
3. Hard to process large quantity of data

Question 9

What is the advantage of using a sample?

Answer 9

• Less time consuming and expensive than a census
• Fewer people have to respond
• Less data to process in a census

Question 10

What is the disadvantage of using a sample?

Answer 10

• The data may not be accurate
• The sample may not be large enough to give information about small subgroups of the population

Question 11

The size of the sample can affect the validity of any conclusion drawn:

Answer 11

• Size of the sample depends on the required accuracy and available resources
• Generally, the larger the sample the more accurate it is, the greater resources you need
• If the population is varied, you need a larger sample than if the population were uniform
• Different samples can lead to different conclusions due to natural variation in a population

Question 12

What is the sampling units?

Answer 12

Individual units of a population

Question 13

What is a sampling frame?

Answer 13

Often sampling units of a population are individually named or numbered to form a list

Question 14

A supermarket wants to test a delivery of avocados for ripeness for cutting them in half

Suggest a reason why the supermarket should not test all the avocados in the delivery:

Answer 14

Testing all avocados would mean that there would be none left

Question 15

The supermarket tests a sample of 5 avocados and finds that 4 of them are ripe.

They estimate that 80% of the avocados in the delivery are ripe

Suggest one way that the supermarket could improve their estimate

Answer 15

They could take a larger sample

e.g 10 avocados

give better estimate of overall population of ripe avocados

Question 16

A factory makes safety harnesses for climbers and has an order to supply 3000 harnesses

The buyer wishes to know that the load at which the harness breaks exceeds a certain figure

Suggest a reason why a census would not be used for this purpose.

Answer 16

The testing process will destroy the harness, so a census would destroy all the harnesses, meaning that there would be no harnesses left for climbers to use

Question 17

The factory tests four harnesses and load for breaking is recorded.

320kg , 260kg , 240kg, 180kg

The factory claims that the harnesses are safe for loads up to 250g. Use the sample data to comment on this chain

Answer 17

The claim is misleading. 250 kg is the mean and median load at which the harnesses in the sample break. So we would expect half of the harnesses to break at a load of less than 250 kg.

Question 18

The factory tests four harnesses and load for breaking is recorded.

320kg , 260kg , 240kg, 180k

Suggest one way in which the company can improve their prediction

Answer 18

Test a large number of harnesses

Question 19

A city council want to know what people think about its recycling centre.

The council decided to carry out a sample survey to learn the opinion of residents

Write down one reason why the council should not take a census

Answer 19

• It would be time-consuming
• Expensive
• Difficult to process the data

Question 20

A city council want to know what people think about its recycling centre.

The council decided to carry out a sample survey to learn the opinion of residents

Suggest a suitable sampling frame

Answer 20

List of residents

Question 21

A city council want to know what people think about its recycling centre.

The council decided to carry out a sample survey to learn the opinion of residents

Identify the sampling units

Answer 21

Each individual resident

Question 22

A manufacturer of microswitches it testing the reliability of its switches. It uses a special machine to switch them on and off until they break

Give one reason why the manufacturer should use a sample rather than a census.

Answer 22

The testing process would destroy the switches, so a census would destroy all the switches, meaning that there would be no switches left to sell.

Question 23

23150 25071 19480 22921 7455

The company claim that its switches can be operated on average of 20 000 times without breaking. Use sample data to comment on this claim

Answer 23

The mean is 19 615.4, less than the stated average. One of the switches survived significantly fewer operations, which suggests that the median of 22 921 might be a better average to take, as it is not affected by outliers. The data therefore supports the company’s claim.

Question 24

Suggest one way the company can improve their predication

Answer 24

Test a larger number of switches

Question 25

A manager of a garage wants to know what their mechanics think about a new pension scheme designed for them. The manager decides to ask all the mechanics in the garage.

Describe the population the manager will use/

Answer 25

All the mechanics in the garage

Question 26

A manager of a garage wants to know what their mechanics think about a new pension scheme designed for them. The manager decides to ask all the mechanics in the garage.

Write down the main advantage in asking all of their mechanics

Answer 26

Everyone’s views will be known