Edexcel A Level Maths: Statistics:复习笔记6.1 Large Data Set

Using a Large Data Set

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

Summary of the Large Data Set

What is the data about?

  • The data consists of samples of data on the weather for eight locations over two different time periods
  • The five UK locations are:
    • Leuchars: town in Scotland
    • Leeming: village in North Yorkshire
    • Heathrow: hamlet in Greater London
    • Hurn: village in Dorest (South West England)
    • Camborne: town in Cornwall (South West England)
  • The three international locations are:
    • Beijing: capital city of China
    • Perth: capital city of Western Australia (state of Australia)
    • Jacksonville: city in Florida (state of USA)
  • The two time periods are:
    • May to October 1987
    • May to October 2015

6-1-1-large-data-set-edexcel-diagram-1

6-1-1-large-data-set-edexcel-diagram-2

What variables are included in the large data set?

  • Daily mean (air) temperature
    • Measured in degrees Celsius (°C) given to 1dp
    • Average of hourly temperature readings between 0900 - 0900 GMT
  • Daily total rainfall
    • Measured in millimetres (mm) given to 1dp
    • Measured for the 24 hours starting at 0900 GMT
    • A trace of rain 'tr' is an amount less than 0.05mm
  • Daily total sunshine
    • Measured in hours (hr) given to 1dp
  • Daily maximum relative humidity
    • Given as a percentage given to the nearest integer
    • A reading above 95% is associated with mist and fog
  • Daily mean windspeed and direction
    • Mean measured in knots (1 kn = 1.15 mph) given to nearest integer and is described using the Beaufort conversion (calm, light, etc)
    • Direction measured in degrees rounded to the nearest 10 and is given as a cardinal direction (north, south, etc)
    • Averaged for 24 hours starting at 0000 GMT
  • Daily maximum gust and direction
    • Measured using the same units as windspeed
    • The maximum instantaneous speed over the 24 hours
  • Cloud cover
    • Measured in Oktas (eighths of the sky covered by cloud)
  • Daily mean visibility
    • Measured in decametres (1 Dm = 10 m) horizontally
  • Daily mean pressure
    • Measured in hectopascals (1 hPa = 100 Pa = 1 millibar)

Is the data complete?

  • There are missing or unknown pieces of data
    • These are listed as 'n/a' or '-'
    • The total daily total sunshine, mean windspeed and maximum gust is unknown for the first half of May 1987 for the UK cities
    • The data should be cleaned before samples are taken
  • The three international cities only contain date for:
    • Daily mean temperature, daily total rainfall, daily mean pressure and daily mean windspeed

What are some of the important features?

  • Consider which locations are closer to the equator
  • Consider which locations are near a coast
    • Jacksonville, Perth, Camborne, Hurn, Leuchars are near the coast
  • Consider which locations are in each hemisphere
    • Perth is in the southern hemisphere so have winter when UK has summer
  • Consider which variables are discrete and which are continuous
    • Cloud cover is discrete
  • You can use 0 or 0.025 for rainfall that is listed as 'tr'
  • The great storm of 1987 happened 15-16 October in UK
    • The wind speeds were high at this time
    • The south of England was affected
    • This will skew some variables (wind/gust/rainfall)
    • This won't have much impact some variables (sunshine/cloud cover)
      • October in the UK is normally cloudy and have less sunshine
    • Don't worry about remembering the exact dates of this but it is something to be aware of
  • Consider the number of days in each month
    • 30 days in June and September
    • 31 days in May, July, August and October
    • In total the LDS covers 184 days

Worked Example

Using the large data set, Dylan collects data on the daily total sunshine in Leuchars from May to October 1987 by taking a random sample of 30 days.

(a) Using your knowledge of the large data set, explain why Dylan will have to first clean the data before taking a sample.
(b) Dylan calculates the mean value from his sample to be 25.3 hours. Using your knowledge of the large data set, explain how you know Dylan has made a mistake.

 

(a) Using your knowledge of the large data set, explain why Dylan will have to first clean the data before taking a sample.

6-1-1-summary-of-the-large-data-set-we-solution-part-1

(b) Dylan calculates the mean value from his sample to be 25.3 hours. Using your knowledge of the large data set, explain how you know Dylan has made a mistake.

6-1-1-summary-of-the-large-data-set-we-solution-part-2

 

 

转载自savemyexams

更多Alevel课程
翰林国际教育资讯二维码