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. See more on this under Resources.

## 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, any statistics calculated from a good sample can be used to describe the whole population. This is called **inference**.

For a sample to be useful it must be:

**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.**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 have taken a sample from a given population, you would then analyse that data you have collected and gather statistics. How you present data and interpret your findings is very important – see Data Representation & Interpretation.

Note that samples can be taken with or without replacement. Without replacement means that, once the member has been selected once, it will be not be returned in the current sample. This prevents a single member being selected twice in one sample.

## Methods of Sampling

**Simple Random Sampling –**a selection process where each member of the population has an EQUAL chance of being selected.**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.**Systematic Sampling –**a technique where the sampling starting point is chosen randomly and the rest of the sample is chosen periodically thereafter.**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.**Opportunity Sampling –**or convenience sampling, is obtained when members from a given population are willing to participate in the investigation. Examples include radio or television phone-ins.

## Examples

**Example 1 (Simple Random)**

Suppose a given company has 50 employees. The company would like to know if the employees are happy with the restaurant facilities. A sample of 10 employees are questioned to find out their views. 50 balls labelled with staff numbers are put into a bag, shaken and 10 removed without replacement. This is an example of simple random sampling. Every combination of 10 balls is equally likely. The **sampling frame** is the list of employee numbers. Note that the sampling frame is a list of all members of a population. Quite often, the biggest problem with simple random sampling is having a complete and accurate sampling frame.

**Example 2 (Systematic)**

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 in chosen at random and turns out to be 122. The 122nd person on the list is the first member of the sample. 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.

**Example 3 (Stratified)**

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. 17 students of those sampled identify as female in a stratified sample – this is 34% of 50.

**Example 4 (Quota) **

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. 60% of the sample should be women of which half should be under 45. Of the men interviewed, 20% should have beards. This is an example of quota sampling.