Population and samples

In a nutshell

When carrying out a statistical survey, different types and amounts of data can be collected. The population is the whole set of the items or individuals that are of interest. A census measures every member of the population. A sample measures only a subset of the population, and these measures are used to estimate measures for the population. There are advantages and disadvantages of using a census and using a sample.

Definitions

There are various definitions you need to know when working with data.

NAME	DEFINITION
Population	The whole set of items or individuals of interest.
Census	A measurement or observation from every member of the population.
Sample	A selection of measurements or observations from a subset of the population.
Sampling units	The individual items or members of the population.
Sampling frame	A list of all the sampling units in the population.
Parameter	A population parameter is a value that can be calculated using the whole population. It summarises everything known about the population.
Statistic	A value that can be calculated from a sample. A statistic can be used to estimate a parameter.

Census and sample

If data is collected from the entire sampling frame, i.e. the whole population, it is called a census. A census can be time consuming and expensive, however the information gathered would be representative of the population. It is usually quicker, easier and cheaper to take a sample, but it is important to ensure that the sampling method creates a sample which is representative of the population.

	ADVANTAGES	DISADVANTAGES
Census	It gives a completely accurate result.	It is time consuming and expensive. Cannot be used when the testing process destroys the items in the population. It is difficult to process large quantities of data.
Sample	The process is less time consuming and cheaper. Less data to process.	It may not give a completely accurate result. The sample may not be large enough to represent the different subgroups of the population.

Example 1

A battery manufacturer wants to test the lifetime of the batteries they make by seeing how long they last. Should they use a census or a sample? Given a reason for your answer.

A census would require all the batteries to be used and they would consequently have no more batteries left to sell.

Therefore, the manufacturer should use a sample.