Collecting Data & Sampling (AQA Level 3 Mathematical Studies (Core Maths)): Revision Note

Collecting Data & Using 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

What are the advantages and disadvantages of using a population?

• A census is when data is collected from every member of the whole population

• Advantages of using a population

  • Accurate results as every member/item of the population is used

    • In reality it would be close to every member for practical reasons

  • All options/opinions/responses will be included in the results

• Disadvantages of using a population

  • Time consuming to collect the data

  • Expensive due to the large numbers involved

  • Large amounts of data to organise and analyse

What are the advantages and disadvantages of using a sample? 

• The advantages of using a sample

  • Quicker to collect the data

  • Cheaper as not so much work involved

  • Less data to organise and analyse

• The disadvantages of using a sample

  • A small sample size can lead to unreliable results

    • The reliability of a sample can be improved by taking a larger sample size

  • A sample can introduce bias

    • This is particularly a problem if the sample is not random

  • A sample might not be representative of the population

    • Only a selection of options/opinions/responses might be accounted for 

    • The members/items used in the sample may all have similar responses

• It is important to recognise that different samples (from the same population) may produce different results

  • A larger sample size will increase the reliability

Sampling Methods

What sampling techniques do I need to know? 

• There are a number of different types of sampling methods, these include

  • Simple random sampling

  • Stratified sampling

  • Cluster sampling

  • Quota sampling

• You should know

  • How each sampling method is carried out

  • The strengths and limitations of each method

What is simple random sampling?

• In simple random sampling every member from the population has an equal probability of being selected for the sample

• Method

  • Uniquely number every member of a population

  • Randomly select n different numbers using a random number generator

• Strengths

  • Useful when you have a small population or want a small sample

• Limitations

  • Time-consuming if the sample or population is large

  • May not give a sample that is representative of the whole population

  • Cannot be used if it is not possible to number or list all the members of the population

What is stratified sampling?

• Stratified sampling is where the population is divided into groups based on characteristics that may affect the investigation, e.g. age, and a random sample is taken from each group 

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

• Method

  • Calculate the number of members sampled from each stratum

    • 

  • Take a random sample from each group

• Strengths

  • Useful when there are very different groups of members within a population

  • The sample will be representative of the population structure

  • The members selected from each stratum are chosen randomly

• Limitations

  • This can not be used if the population can not be split into groups or if the groups overlap

What is cluster sampling? 

• Cluster sampling is 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

• Method

  • Identify the clusters within the population

  • Randomly select a number of clusters

  • Use all members in the selected clusters

• Strengths

  • Easy to complete

  • Cheaper and quicker than some other types of sampling

  • When appropriate clusters are used, the sample will be representative of the population

• Limitations

  • If appropriate clusters are not used, the sample may not be representative of the population

What is quota sampling?

• Quota sampling is where the population is split into groups (similar to stratified sampling) and members of the population are selected until each quota is filled

• Method

  • Calculate how many people you need from each group

  • Select members from each group until that quota is filled

    • The members do not have to be selected randomly,

      e.g. members of the public walking past that fit that group may be selected

• Strengths

  • Quick and inexpensive to complete

  • Useful when a sampling frame is not available

• Limitations

  • Some members of the population might choose not to be included in the sample

  • Members may not have been selected randomly