WJEC Maths for AS: Applied sample

1 Statistical sampling 10 1.1 The terms population and sample In order to prove or disprove a hypothesis or provide an answer to a question, data must be collected. It is usually too expensive and time consuming to measure or observe the whole set you are interested in (called the population). Instead a smaller set is used (called a sample) but it is essential that this sample is representative of the larger population. Here are some important deϐinitions: Population – all members of the set that is being studied or has data collected about. So, for example, if you wanted to do a survey using all the students in your school then the population would be every student in your school. It is usually too costly and time consuming to survey the whole population, so a smaller set called a sample is used. Sample – a smaller subset of the population that is used to draw conclusions about the population. As the sample is usually much smaller than the population, errors and inaccuracies can result when drawing conclusions about the population. 1.2 Using samples to make informal inferences about the population Once a representative sample has been obtained, it can be used to make inferences about the population. Inferences are conclusions reached on the basis of evidence and reasoning. You do have to be careful when making inferences as the following example shows: Example 1 The lake shown below contains a variety of ϐish. The owner of the lake would like to advertise the lake for ϐishing and wants to know about ϐish population of the lake.