Sampling data

As we have seen, the subset of the population you choose to work with is called a sample. You can select a sample from a population in many different ways. Not all samples will be equally useful for generalising results, so how you choose the sample is very important.

Simple random sample

As the name implies, this is the simplest way of obtaining a representative sample from a population. In a simple random sample, each member of the population has an equal chance of being selected – that is, no member of the population is systematically excluded from the sample, nor are particular members of the population more likely to be included. Common examples for obtaining random samples are drawing names from a hat and drawing lottery tickets. Each member of the sample is also selected independently – that is, the selection of a member in no way influences the selection of another member.

Systematic sampling

Sometimes it is easier to apply a system to the sampling. For example, imagine we want to find out how satisfied customers are with the services provided by a sports centre. We know that the centre services approximately 600 members per day, so if we wished to survey a sample of 60 people, we could survey every tenth person leaving the centre.

Uses of sampling

A sample can tell us something about a population. Sampling and analysing the results gained from investigating the sample is an important part of most scientific research. For example, some environmental scientists investigate particular species of plants or animals to find out if they are  thriving, stable or on the way to extinction. For example, scientists are investigating the health of green frogs that live in a particular area of Queensland. They need to find out how many there are in that area, their weight and the length of their hind legs. It would be impossible to find and measure every green frog so they analyse just a sample of the green frog population.

An important part of any research is ensuring that the observations recorded relate to the questions the researcher is trying to answer. Data from the frogs' mean weight and the length of their hind legs allow scientists to predict statistics for the population of green frogs. These statistics cannot be measured exactly; they can only be estimated from the sample. This raises an important issue regarding accuracy for scientists, an issue to be studied at a later date.

Example

A light bulb manufacturer wants to make a statement about the life of the light bulbs they produce. Obviously, they cannot test every light bulb to see how long it lasts. So, they select a random sample of bulbs and test their longevity. From these results, they can make some claims regarding the life of the bulbs.

Students at this level need to understand that when one takes a sample, all one can describe with any accuracy are the statistics on that sample. Further samples can and probably will give different results.