Sampling

In terms of statistics, a population is a group of people that the data collector is interested in. A sample is then selected as a smaller group chosen from the population. Statisticians select a sample by naming/numbering the population and creating a list which is then known as a sampling frame.

There are four types of samples that A Level Mathematics students will need to be aware of random samples - simple, systematic, Non - random samples - quota and opportunity, with brief descri ptions given below:

Random samples - can be simple (generate random numbers for example) or can be systematic - population is numbered and sampling units are randomly selected at regular intervals.

Non-random samples - Quota sample (select a predetermined amount of sampling units that have certain defined requirements) or use an opportunity sample where conveniently located sampling units are selected provided they meet requirements of criteria.

Why use samples?

Another option available to statisticians is the use of a census. In order to carry out a census, a lot of time would be needed and a large amount of data would be collected and would then need to be processed.

Collecting a sample is a lot quicker and cheaper than a census but note - a sample is not always a true representation of a population and can lead to bias.

Stratified sampling is a form of random sampling where a population is divided into strata on the basis of available information. A sample is then drawn independently from the stratum. The chances of drawing a a biased sample would be vastly reduced via stratified sampling but this sampling method does requires advance knowledge about the available population which is not always easy to come by.

Worked Example

A local gym manager wishes to obtain the views of gym users concerning the gym equipment. She decides to conduct a survey of 40 of the gyms 246 members of whom 113 identify as male.

How could the gym manager go about this?

Stratified random sampling would be a good sampling method to use here and she would first need to calculate the number of male members and the number of female members.

Of the gym members 113 are male so 133 are female so she needs

Men: (113/246) x 40 =18

Women: (133/246) x 40 =22

Therefore the gym manager could take a random sample of 18 men and 22 women. She could assign each gym member a random number agaisnt their gym membership and select that way.