The population is the group that you want to find information about. Sometimes populations are so large that we use a smaller group, known as a sample, to make predictions about the whole population. We would use a sample rather than the whole population because finding out information for the whole population would be very time consuming and extremely expensive.

Let’s now have a look an example of a sample being used. Suppose that I work for the forestry commission and we are trying to work out how many trees in a particular forest are infected by a certain type of fungus. There are 1200 tree in the forest. The worker says that it is going to take too long to look at every single tree. Instead, he takes a sample of 200 trees and sees how many of them are infected by the fungus. After completing the sample, we can predict how many trees in the whole forest are infected by the fungus.

Let’s now continue the example and suppose that 72 of the 200 trees in the sample are infected by the fungus. How many trees in the whole forest are infected by the fungus?

In order to find an estimate for the number of trees that are infected by the fungus, we need to see how many times larger the population is compared with the sample size that we took. We find out how many times larger the population is compared with the sample by dividing the population by the sample. The sample size was 200 and the population of trees in the forest is 1200. Therefore, we complete the following calculation:

Let’s now have a look an example of a sample being used. Suppose that I work for the forestry commission and we are trying to work out how many trees in a particular forest are infected by a certain type of fungus. There are 1200 tree in the forest. The worker says that it is going to take too long to look at every single tree. Instead, he takes a sample of 200 trees and sees how many of them are infected by the fungus. After completing the sample, we can predict how many trees in the whole forest are infected by the fungus.

Let’s now continue the example and suppose that 72 of the 200 trees in the sample are infected by the fungus. How many trees in the whole forest are infected by the fungus?

In order to find an estimate for the number of trees that are infected by the fungus, we need to see how many times larger the population is compared with the sample size that we took. We find out how many times larger the population is compared with the sample by dividing the population by the sample. The sample size was 200 and the population of trees in the forest is 1200. Therefore, we complete the following calculation:

The population is 6 times larger than the sample. The next step is to multiply the number of trees infected in the sample (72) by the number of times that the population is greater than the sample (6).

Therefore, an estimate for the number of trees in the forest that are infected by the fungus is 432. We need to note that this is only an estimate and it is not the actual number of trees that will have been infected by the fungus.

**Positives & Negative of Population & Sampling**

The benefits of using the population when collecting data is that everyone or everything in the population is accounted for/ asked/ surveyed. In the above tree example, if we would have used the whole population (all of the trees in the forest), we would know the exact number of trees that are infected by the fungus, thus meaning that our results are 100% accurate. Whereas, when using a sample, we only have an estimate for the number of trees that have been infected by the fungus and this estimate may or may not be close to the actual number of trees that are infected by the fungus.

A massive disadvantage of using a population is that it will take an extremely long time to collect the data. Also, it is very costly to obtain the data. In our tree example, our worker would have to check 1200 trees, which is 6 times as many trees as the number of tree that he checked in the sample. This is going to take 6 times as long and is going to be 6 times as expensive.

This brings us on to advantages of sampling, which are essentially the opposite of the disadvantages of using a population. The advantages of sampling are that sampling is cheaper and quicker than using the population. Using a sample of the trees will take a sixth of the time that it takes to check the population of trees and it should be a sixth of the cost.

The disadvantages of sampling are essentially the opposite to the advantages of using the population. Sampling is only estimate, which means that the results will probably not be 100% accurate. The accuracy of the estimate from the sample can be improved by increasing the sample size. So, for our example, we could have had 300 trees in our sample rather than 200 trees. We can also increase the accuracy of the sample by making sure that the sample that we select is representative of the population. With our tree example, we should make sure that the sample contains the same proportion of the different varieties of trees in the forest. For example, if 50% of the trees were conifers, 30% of the trees were conker trees and 20% were oak trees, we should make sure that the percentages in the sample match up; so in the sample 50% of the trees should be conifers, 30% of the trees should be conker trees and 20% of the trees should be oak trees. This is because if we were to make the percentages of each tree different in the sample to the population, the estimate produced from the sample will likely be wrong. This is because it could be the case that one type of tree is very susceptible to being infected by the fungus and another tree is quite resistant to the fungus. If the sample contains a greater proportion of trees from the variety that are quite resistant to the fungus, it will result in a lower number of trees in the sample being infected, which will mean that our estimate will underestimate the number of trees that are going to be infected by the fungus. The opposite would be true if we were to have a greater proportion of trees from a variety that are more susceptible to being infected by the fungus in the sample. This is because it would mean that there are more trees that are infected in our sample, which will mean that the estimate will overestimate the number of trees in the population that are infected by the fungus. Another example of where the sampling method could go wrong in our tree example would be to only choose trees that are in one specific location in the forest. It could be the case that the fungus is more likely to be present in certain parts of the forest. Therefore, if we only choose trees from one section of the forest our estimate will likely be wrong.

Another negative of using samples is that sometime individuals or organisations that are undertaking the sample may choose a sample that supports their agenda. For example, a housing developer may be undertaking a survey to see what people’s opinions are to new houses being built in a certain location. The housing developer will want to make sure that the results that they find are supportive of what they want to take place. This means that they are likely to choose individuals to fill out the survey that are more for the development than individuals that are strongly against the development taking place. This is known as bias and this is why surveys or research is usually carried out by independent authorities.