1.1 Population and samples Flashcards
What does population mean in statistics?
Whole set of items that are of interest
Examples of populations
- Items manufactured by a factory
- All the people in town
What can be obtained from a population?
Information
What is raw data?
Unprocessed information
What is a census?
Observes or measures every member of a population
What is a sample?
Selection of observations taken from a subset of the population which is used to find out information about the population as a whole
What is the advantage of using a census?
It should give a completely accurate result
Disadvantages of using a census
- Time-consuming and expensive
- Cannot be used when testing process destroys the item
- Hard to process large quantity of data
What is the advantage of using a sample?
- Less time consuming and expensive than a census
- Fewer people have to respond
- Less data to process in a census
What is the disadvantage of using a sample?
- The data may not be accurate
- The sample may not be large enough to give information about small subgroups of the population
The size of the sample can affect the validity of any conclusion drawn:
- 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
What is the sampling units?
Individual units of a population
What is a sampling frame?
Often sampling units of a population are individually named or numbered to form a list
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:
Testing all avocados would mean that there would be none left
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
They could take a larger sample
e.g 10 avocados
give better estimate of overall population of ripe avocados
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.
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
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
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.
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
Test a large number of harnesses
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
- It would be time-consuming
- Expensive
- Difficult to process the data
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
List of residents
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
Each individual resident
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.
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.
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
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.
Suggest one way the company can improve their predication
Test a larger number of switches
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/
All the mechanics in the garage
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
Everyone’s views will be known
