Large Data Set (OCR A Level Maths: Statistics)

What is a large data set?

• As part of your course there is a large data set that you can use
• It contains lots of information
• You are not expected to memorise any results from the data
• You will have an advantage if you are familiar with the large data set
  • Understand what the variables are
  • Understand the terminology used
  • Understand the context
• You will not get a copy of the large data set in your exam
  • if you are required to calculate anything using the large data set you will be given an extract within the question

What skills can I practice with a large data set?

• Cleaning data
  • There might be missing data
  • You could identify outliers and question their validity
• Sampling and hypothesis testing
  • You can practice different methods of sampling using the data
  • You could use a sample to test a hypothesis
• Statistical measures and diagram
  • You could calculate summary statistics for different variables
  • You could create different diagrams
  • You can interpret the summary statistics and diagrams (as it is real data you could explore the context behind the results)
  • You could compare summary statistics and diagrams

Do I have to use spreadsheets and other technology?

• You will not be assessed on using spreadsheets
  • However, it is a useful skill for your future career
• You could use technology to calculate the summary statistics and create the statistical diagrams
  • This will help you to practice these skills whilst using real data
  • Spreadsheets can calculate summary statistics
  • In the exam you could use the statistics mode on your calculator

What is the data about?

• The LDS consists of four data sets covering the age structure of the population in England and Wales and the method of travel to work from the censuses of 2001 and 2011
• The data is regional and comes from 348 districts covering all of England and Wales which are referred to as the Local Authority Districts (LAD) or Unitary Authorities (UA)
  • The unitary authorities were created by combining some LADs due to change over the 10 years between 2001 and 2011
• The 348 districts are grouped into the following regions

North East   (12 districts)

North West (39 districts)

Yorkshire & The Humber (21 districts)      

East Midlands (40 districts)

West Midlands (30 districts)         

East of England (47 districts)        

London (33 districts)        

South East (67 districts)  

South West (37 districts)

Wales (22 districts)

What data collection methods were used?

• The data were collated from the 2001 and 2011 censuses
  • The census is carried out every 10 years and collects data from every contributing member of the population across England and Wales
  • It gives the best possible estimate for an overview of the population
• The 'method of travel' data sets encompass all people who were in employment at the time of the census collection
  • The method of travel concerns the part of their journey to work where they travelled the furthest
• The age structure data set is taken from the date of birth question on the survey
• The age is taken to be the person's age on their last birthday before the time of the census collection
  • A person of less than a year old was recorded at 0
  • In 2001 a data entry of over 110 was treated as invalid
  • In 2011 a data entry of over 115 was treated as invalid

What are some of the important features?

• Take some time to review the age structure boundaries
  • They are not even and have widely varying class widths
  • Notice how the class widths for teenagers are particularly small whilst those for ages 30 – 59 are much wider
  • This means looking at a normal frequency diagram or population pyramid would be misleading, instead you should use a histogram and calculate frequency densities
• Look at the different types of districts and be aware of how the method of travel to work changes between them
  • Non-metropolitan district in England (E08) refers to towns and small cities
  • Metropolitan boroughs (E08) refers to big cities is certain areas of England
  • London borough (E09) refers to all parts of London
  • Be aware that there are other Unitary Authorities in England (E06) that could be either a metropolis or a smaller city
  • W06 refers to a unitary authority in Wales, these are mostly rural except for the districts of Cardiff and Newport
• Consider the variation in age in rural areas compared to metropolises, think about why big cities and the London districts might have less variation in age
• Consider the method of travel to work in rural areas compared to metropolises, think about why big cities and the London districts might have more people who use public transport
• Look at the change in use of public transport from 2001 to 2011
  • Consider some reasons why more people may use public transport in 2011, could there have been improvements in those areas or perhaps government incentive schemes?
• Watch out for correlation, the values are given as direct numbers so as the population increases so will the method of travel to work
  • You would need to look at the proportion to get a better idea of correlation