# 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

#### 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.

(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.