Populations & Samples (AQA Level 3 Mathematical Studies (Core Maths))

Populations & Samples

What is a population?

• A population refers to the whole set of things which you are interested in

  • E.g. if a teacher wanted to know how long pupils in year 11 at their school spent revising each week then the population would be all the year 11 pupils at the school

• Population does not necessarily refer to a number of people or animals

  • E.g. if an IT expert wanted to investigate the speed of mobile phones then the population would be all the different makes and models of mobile phones in the world

What is a sample?

• A sample refers to a selected part (called a subset) of the population which is used to collect data from

  • E.g. for the teacher investigating year 11 revision times a sample would be a certain number of pupils from year 11

• A random sample is where every item in the population has an equal chance of being selected

  • E.g. every pupil in year 11 would have the same chance of being selected for the teacher's sample

• A biased sample is where the sample is not random

  • E.g. the teacher asks pupils from just one class

• One or more samples can be used to make judgements about a population

  • These judgements may have varying degrees of certainty dependent on the sample used

  • It is important that the samples are random, to improve the degree of certainty of any judgements made

How do I take a random sample of a population?

• There are three types of random sampling as explained below

• Simple random sampling: a sample is formed by choosing members of a population completely at random

  • Every member of a population is assigned a unique number and 𝑛 different numbers are selected using a random number generator or a form of lottery

• Stratified sampling: a sample is formed by diving the population into groups based on characteristics that may affect the investigation, e.g. age, and taking a random sample from each group 

  • The proportion of a group that is sampled is equal to the proportion of the population that belong to that group

  • The number of members sampled from each stratum (group) is calculated using

• Cluster sampling: where the population already naturally falls into groups (clusters), e.g. streets in a town, a random number of clusters are selected and all members from within these clusters are used in the sample