Statistical Sampling

What is a population?

When carrying out an experiment, the population is the set of all items that could be included. For example, if someone was investigating the average height of a maths student in the UK, then the population would be every maths student in the UK. 

What is a census?

A census is when every member/item of a population is included in an experiment/investigation. For example, if someone was investigating the average height of a maths student in the UK then to take a census they would have to find the height of every maths student in the UK.

What are the advantages and disadvantages of a census?

The advantages of using a census are:

• It includes the whole population so it is free from bias
• It gives plenty of data to perform meaningful analysis

The disadvantages of using a census are:

• It is be expensive and  time consuming when the population is large
• There could be too much data to analyse
• If the population involves one-time-use items (such as fireworks) then taking a census could use up all of the items

What is a population parameter?

A population parameter is a numerical value associated with the population. It could be the mean, median, range, standard deviation, maximum value, population size, etc.

What is a sample?

A sample is a collection of members from a population. 

What is the use of a sample?

It is usually difficult or impossible to find the exact value of a population parameter. Therefore a sample is taken from the population and a statistic is calculated to estimate the parameter. The could be the sample mean, sample median, sample variance, etc.

What is meant by a random sampling method?

A sampling method is called random if every method of the population has a chance of being selected as part of the sample. Random sampling is used to minimise the risk of introducing bias into the experiment.

What is simple random sampling?

Simple random sampling is where every member of a population has an equal chance of being included as part of the sample. Another way to think of this is, every group of members of a given size has an equal chance of being used as the sample.

How do I perform simple random sampling?

The easiest way to perform simple random sampling is using a lottery method. Assign a number to each member of the population and then randomly select numbers until the sample is filled.

What are the advantages and disadvantages of simple random sampling?

The advantages of simple random sampling include:

• It minimises the risk of introducing bias
• It can be quick to do for a small sample when the population is also small

The disadvantages of simple random sampling include:

• It may not be representative of the population (it is possible that every member of the sample share a common characteristic)
• It may not be possible to list all the members of the populationIt can take a long time to assign numbers if the population is large

What is systematic sampling?

Systematic sampling is where members are listed and members are chosen at regular intervals. 

How do I perform systematic sampling?

Divide the population size by the sample size to get the size of the interval. Choose a starting point and then choose every member using the same interval.

What are the advantages and disadvantages of systematic sampling?

The advantages of systematic sampling include:

• It is easy to perform with a list of the population
• It can be quick to do for a small sample when the population is also small

The disadvantages of systematic sampling include:

• It may not be representative of the population (it is possible that every member of the sample share a common characteristic)
• It is only random if the first member if randomly chosen

What is stratified sampling?

Stratified sampling is where members of a population are put into groups based on a characteristic. Members are chosen for the sample so that the proportion of the population that share the characteristic is the same for the sample.

How do I perform stratified sampling?

1. Put the members into groups.
2. Find the proportion of the population that are in each group.
3. Multiply the proportion by the sample size to find the number of members from each group that should be included in the sample.
4. Use simple random sampling to choose the members from each group.

What are the advantages and disadvantages of stratified sampling?

The advantages of stratified sampling include:

• It gives a sample that is representative of the population
• It is random so reduces bias

The disadvantages of stratified sampling include:

• It may not be possible to split the population into disjoint groups
• A list of the population is not always possible

What are some examples of non-random sampling methods?

Cluster sampling is where a population is split into groups and then only one of the groups is used as the sample. For example, if there are 10 maths classes in Year 11 then choosing just one as a sample is cluster sampling.

Quota sampling is similar to stratified except the members from each group are not chosen randomly. For example, 15 fish from a lake are required for a sample. 10 should be trout and 5 should be cod. The person doing the experiment might just use the first 10 trout and the first 5 cod they catch as their sample.

Convenience sampling is where the person doing the experience using whatever is the easiest method. For example, they could ask the first 100 people to walk past them on a street. 

When is quota sampling more useful than stratified sampling?

Quota sampling is more useful than stratified sampling when it is not possible to obtain a list of the population or if the population is large.