Population definition
The whole set of items that are of interest.
Give two examples of populations
The items manufactured by a factory
All the people in a town
What can be obtained from a population?
Information
Information obtained from a population is known as …
Raw data
Census definition
A census observes or measures every member of a population.
Sample definition
A selection of observations taken from a subset of the population which is used to find out information about the population as a whole.
What are the advantages of a census?
• It should give a completely accurate result.
What are the disadvantages of a census?
- Time consuming and expensive
- Cannot be used when the testing process destroys the item
- Hard to process large quantity of data
Large data sets are produced which:
- Are difficult to manage without computers
- And can include missing pieces of data
What are the advantages of a sample?
- Less time consuming and expensive than a census
- Fewer people have to respond
- Less data to process than in a census
What are the disadvantages of a sample?
- The data may not be as accurate
* The sample may not be large enough to give information about small sub-groups of the population
What will the size of the sample affect?
The validity of any conclusions drawn
What does the size of the sample depend upon?
The required accuracy and available resources
Generally, the larger the sample …
The more accurate it is, but you will need greater resources
In what cases will you need a larger sample?
If the population is very varied, you need a larger sample than if the population were uniform
Why can different samples lead to different conclusions?
Due to the natural variation in a population
What are individual units of a population called?
Sampling units
What are sampling units?
Individual units of a population
Often sampling units of a population are individually named or numbered to form a list called a …
Sampling frame
What is a sampling frame?
Often sampling units of a population are individually named or numbered to form a list called a sampling frame.
Example 1
A supermarket wants to test a delivery of avocados for ripeness by cutting them in half.
a) Suggest a reason why the supermarket should not test all the avocados in the delivery.
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.
b) Suggest one way that the supermarket could improve their estimate.
a) Testing all avocados is a census, which will destroy all the product so that there is nothing to sell.
b) To improve estimate:
- Take a larger sample
- Sample numerous deliveries
- Sample over time
What are the three methods of random sampling?
- Simple random sampling
- Systematic sampling
- Stratified sampling
What are the key features of random sampling?
- Every member of the population has an equal chance of being selected.
- The sample should therefore be representative of the population.
- Random sampling also helps to remove bias from a sample.
How can a simple random sample be carried out?
- You need a sampling frame (usually a list of people or things)
- Each person or thing is allocated a unique number and a selection of these numbers is chosen at random.
What are the two methods of choosing the numbers in a simple random sample?
- Generating random numbers (using a calculator, computer or random number table)
- Lottery sampling
