Sampling

Before reading up on sampling below, it is important to know that your syllabus may require that you take a sample from a dataset that you are already familiar with. For example, the large dataset used by Edexcel is based on weather data samples provided by the MET Office. The more familiar you are with the dataset, the more of an advantage you have when tackling these questions. It is possible that you may need to recall certain trends in the data, for example. 

What is Sampling?

Sampling is essentially extracting samples. Suppose that you would like to know the average height of the human population. Evidently, it is impossible to know this because you cannot know the height of every living human being. In which case, you cannot calculate its mean. Click here to see the Average Human Height Worldwide. So, how is it possible to know this information? Instead of measuring the height of everyone, we could measure the height of a sample. If the sample is chosen well,  the sample represents the entire population well. Subsequently, we can use any statistics we calculate from a good sample to describe the whole population. This is called inference.

For a sample to be useful it must be:

  1. unbiased– this effectively means not too much of one type in a sample. If we are interested in the distribution (spread) of height, our sample should not be restricted to basketball players, for example.
  2. representative size – a sample of two is not sufficient to give an accurate representation of a large population as it is prone to skewing. This means favouring a certain type over others.

Once you take a sample from a given population, you can then analyse that data and gather statistics. How you present data and interpret your findings is very important – see Data Representation & Interpretation. Note that we can take samples with or without replacement. Without replacement means that, once we select a member, they will not be returned to the current population. This prevents us from selecting a single member twice in one sample.

Methods of Sampling

  1. Simple Random Sampling – a selection process where there is an EQUAL chance of selecting each member of the population. See Example 1.
  2. Stratified Sampling – Stratum is another word for class, level or grade. Strata is then the plural of stratum. Stratified sampling is a sampling technique that preserves the given strata proportions. See Example 2.
  3. Systematic Sampling – a technique where the sampling starting point is chosen randomly and the rest of the sample is chosen periodically thereafter. See Example 3.
  4. Quota Sampling – this type of sampling requires the sampler or interviewer to complete their investigation according to a set of instructions. The instructions will usually specify which quotes are to be met. See Example 4.
  5. Opportunity Sampling – or convenience sampling, is where members from a given population are willing to participate in the investigation. Examples include radio or television phone-ins.

Examples

Suppose a company has 500 employees. The company would like to know if the employees are happy with the restaurant facilities. The company wants to question a sample of 100 employees.  Hence, 500 balls labelled with staff numbers are put into a bag, shaken and 100 removed without replacement. This is an example of simple random sampling since every combination of 100 balls is equally likely. Note that the sampling frame is a list of all members of a population. Evidently, the sampling frame is the list of employee numbers.  Quite often, the biggest problem with simple random sampling is not having a complete and accurate sampling frame.

Suppose we wish to choose 7 individuals from a list of 350 people. Each individual on the list is identified by a unique list number. A number from 1 to 350 is chosen at random and turns out to be 122. The 122nd person on the list is the first member of the sample. Then the remaining members of the sample are chosen by going up in 50s in the list. It follows that 122nd, 172nd, 222nd, 272nd, 322nd, 22nd and 72nd members of the list form the sample. This is an example of systematic sampling.

There are 400 students on the Mathematics programme at a University. 34% of these students identify as female. A sample of 50 students is chosen to find out how many extra reading hours the students complete. We must take 17 of the students who identify as female in the stratified sample. This is because 17 is 34% of 50. This is stratified sampling.

Your boss asks you to complete some street interviews. You should stop people on the street and ask them which is their favourite brand of washing powder. Your instructions include firstly that 60% of the sample should be women. Secondly, half of the women should be under 45. Finally, of the men you interview, 20% should have beards. This is an example of quota sampling.

AS Statistics Sampling