Year 10 Statistics Coursework 2004

Year 10 Statistics Coursework 2004An investigation into the Grand Prix Results in the

Years of 1993 until 2003

I am going to investigate the results of the Grand Prix of the years ranging from 1993 until 2003.

My hypothesises: Hypothesis one:In 2003 and new point system was introduced, the drivers are awarded points depending on there final position in the race. Before 2003 the point system went as follows:Place Points awarded1st 102nd 63rd 44th 35th 26th 1

In 2003 the point system was altered so that the first eight people to complete the race are awarded points, as follows:

Place Points awarded1st 102nd 83rd 64th 55th 46th 37th 28th 1

My hypothesis is that if the new point system had been used in previous years the team called Minardi would have done a lot better overall and would be higher up in the league of cars.

I will investigate this by getting the results of some of the Grand Prix from the official formula one website. I will then work out the points this team would have received had the new point system been introduced earlier and see if they would be any higher up.

Hypothesis 2:My second hypothesis is that the more successful the team in the Grand Prix the more popular they will be. I will prove, or disprove, this by handing out a questionnaire around the school. I will access the information about the success of the team from the official formula one website. In my questionnaire people will be ranking the teams on the scale of one to ten, I will take the total of the rankings of each of the teams and

Suzanne Robinson 10DL Page 1

then work out the overall ranking of the team. I will then use spearman’s rank coefficient to calculate how much of a correlation these two pieces of data have. I will also investigate whether I get a better correlation from people who watch formula one and also whether there is a better correlation with the regular viewers of formula one.

Hypothesis 3:My third hypothesis is that drivers tend to perform better when they are racing at their home ground. I will do this by comparing the points the received at their home grounds race in a year compared with the points they received at all of the other tracks. The information about their results will be found on the official formula one website.

The purpose of studying the first hypotheses could be to access which point system is fairest for the formula one constructions, as well as to investigate whether some of the lower budgeted teams have a fair opportunity for their drivers to get a relatively high place in the drivers and or constructors championships. The second hypothesis may be used to prove that people tend to support the more successful teams. The third hypothesis may have a purpose for drivers to see where they perform better and whether they perform well on their home track.

Sampling:For the questionnaire I will need to carefully choose a sample of people within the school. I have chosen to hand out my questionnaire to people from year seven and year eleven, as I will be able to compare the results I get between the different ages. As there is a considerable difference in the amount of students in year seven compared with year eleven I will need to take a stratified sample. I intend to question one hundred people in total. As I am obtaining the results myself this will be primary data.

First I will need to find the total number of pupils:Number of pupils in year seven = 200Number of pupils in year eleven= 164

Total number of pupils = 200+164 = 364

I now need to find the fraction of pupils in each year in order to obtain the number of pupils I will need to ask from each year in the sample of one hundred.

Year Fraction of Pupils Number of pupils in the sample of 100 (rounded

to the nearest whole number)

7Females

Males

92364108

92364 x 100 = 25108


364 364 x 100 = 30

11Females

Males

8836476364

88364 x 100 = 2476364 x 100 = 21

Total 100

This means I will need to give out the questionnaire to:25 female pupils and 30 male pupils from year seven and 24 female pupils and 21 male pupils from year 11.

I will select the pupils I will question using a random sample, for this I will need to give every member from the population a number after they have been put in alphabetical order. The numbers will then be put into random number tables which I will obtain by using the numbers one to one hundred using the random button on a scientific calculator. I will select the numbers by reading the values horizontally – ignoring the values which exceed the total number of pupils in each group until I have the required amount of names of people I will hand out the questionnaire to.

Random number tables:

Year 7 girls:

Person who will be questioned

Un-needed number

Year 7 boys:


56 88 26 90 7770 8 77 68 5968 72 49 33 5437 103 4 83 26

90 74 5 21 9459 49 25 74 1391 89 54 53 3123 37 53 30 84

99 66 18 17 8151 65 93 43 9067 39 93 36 2848 97 25 77 81

63 55 76 37 48100 93 50 58 4020 55 56 98 5962 32 44 13 9


Un-needed number

Year 11 girls:


Un-needed number

Year 11 boys:


Un-needed number

I chose to do use random number table and a stratified sample in this way so that there would not be any bias in the results.


4 84 33 69 9593 46 58 39 9468 72 76 46 5829 57 6 42 63

61 3 59 63 7520 69 79 17 9587 96 9 98 6233 62 29 70 64

72 55 53 96 95 7 69 83 1787 9 97 22 1178 1 2 55 64

82 97 36 39 513 2 39 4 9735 99 84 35 9983 14 31 15 50

Other data:

The other data I will obtain will be taken of the official formula one website, I will need to get results about the results of Minardi as well as the results for particular drivers which were able to race at their home track and also the results for the constructors championships.

Predictions:Hypothesis one:I predict that with the new point system Minardi will have done better in previous years because in some cases the drivers were just under the positions in which they can be awarded points.

Hypothesis 2:I predict that there will be a fairly strong correlation between the popularity of the team and the number of people that support them within my sample, this will mean that people will not favour teams like Minardi but will however favour teams like Ferrari.

Hypothesis 3:I predict that there may be a weak correlation between drivers performance at their home ground because they will want to do well for their country in front of their country’s people.

The females I will be questioning from year seven are as follows:Name Form Sex Year

Bird, Jeremia ABR F 7

Brunning, Abigail MBT F 7

Clifford, Shauna MR F 7

Cood, Nicole CO F 7

Harrington, Amy MR F 7

Hood, Lisa ABR F 7

Humphries, Jessie CO F 7

Hyett, Rebecca ABR F 7

Jeffrey, Stacey RPR F 7

Jeffs, Sarah MR F 7

Letham, Chelsea MR F 7

Maloney, Katie MR F 7

Manfredi, Marianne AKE F 7

Mayhew, Jolene MBT F 7

McGrouther, Connie AKE F 7

Mills, Laura CO F 7

Minton, Melissa ABR F 7

Mortlock, Hannah CO F 7

Morys, Amanda MBT F 7

Murphy, Anna AKE F 7

Nunn, Abigail MH F 7

Peters, Kimberly AKE F 7

Skipp, April MBT F 7

Taylor, Dorothy CO F 7


The females I will be questioning from year eleven are as follows:Name Form Sex Year

Ayres, Molly LA F 11

Ballard, Lucy SBR F 11

Baster, Laura DH F 11

Buckingham, Laura CMI F 11

Curtis, Gemma PJ F 11

Dennis, Kirstie SBR F 11

Harrison, Laura DD F 11

Holmes, Roxanne SBR F 11

Kayley, Kimberly SBR F 11

Mackechnie, Kirsty LA F 11

Matthews, Emily DH F 11

Pearce, Hannah SBR F 11

Porter, Rochelle LA F 11

Purcell, Lindsey LA F 11

Reeve, Hannah PJ F 11

Robson, Ella DD F 11

Smith, Lucy DD F 11

Spellman, Annie DD F 11

Stevens, Hayley SBR F 11

Suckling, Abby PJ F 11

Sutton, Tanya LA F 11

Tinslay, Katherine PJ F 11

Whitbread, Kayley DH F 11

Winstanley, Charlotte SBR F 11

The males I will be questioning from year seven are as follows:Name Form Sex Year

Baker, Jed AKE M 7

Benjamin, Joshua CO M 7

Blackwell, Rowan MBT M 7

Bright, Jack RPR M 7

Cooper, Matthew AKE M 7

Cornish, Chanelle MBT M 7

Couzens, Adam AKE M 7

Dawson, Luke MR M 7

Deal, Innes ABR M 7

Dyer, Steve CO M 7

Edney-Hammond, Haydn ABR M 7

Fisher, Samuel AKE M 7

Holt, Matthew MH M 7

Jacobs, Nathan MBT M 7

Jolley, Cristopher CO M 7

Kane, Joseph MR M 7

Knight, Ryan RPR M 7

Nagorski, Mark MBT M 7

Onslow, Philip AKE M 7

Paton, Daniel ABR M 7

Pease, Thomas MBT M 7

Pollard, Jake ME M 7

Rippingale, Matthew RPR M 7


Name Form Sex Year

Rowlingson, Thomas ABR M 7

Scillitoe, Liam ABR M 7

Sewell, Tom RPR M 7

Seymour, Robert MH M 7

Shadenyi, Anslem CO M 7

Shreeve, Kalebh ABR M 7

Wells, Robert CO M 7

The males I will be questioning from year eleven are as follows:Name Form Sex Year

Baker, Riki DD M 11

Bass, Sean CMI M 11

Boreham, Andrew PJ M 11

Briggs, Tristan PJ M 11

Carter, Oliver DH M 11

Clarke, Christopher PJ M 11

Cood, Gary SBR M 11

Corbett, John DD M 11

Cotton, Patrick CMI M 11

Crane, Harry PJ M 11

Curtis, Jamie DH M 11

Gibbs, Roscoe SBR M 11

Longcroft, Samuel LA M 11

McStravick, Sean CMI M 11

Mitchell, Thomas PJ M 11

Pauley, Jacob LA M 11

Simonds, Andrew PJ M 11

Skipper, Ian DD M 11

Turner, Robert PJ M 11

Williamson, Matthew DD M 11

Wright, Samuel LA M 11

On the next page is a copy of the questionnaire I will hand out to these people.


Year 10 Statistics Coursework 2004Questionnaire for the investigation into the Grand Prix

Results in the Years of 1993 until 2003

1. Do you ever watch formula one?Yes

No

2. Do you watch it regularly? Yes

No

3. Do you support a certain team? Yes

No

4. If you answered yes to question 3,which team do you support?McLaren

Williams

Ferrari

Minardi

Renault

Toyota

BAR Honda

Jaguar

Jordon


Sauber

5. What is the reason for supporting this team?

Their success

My parents support them

My friends support them

I like the driver(s)

Other (please specify)………………

6. If the team you supported did badly next year would you still support them?

Yes

No

7. With one being the best team and ten being the worst, rate the following teams:

McLaren

Williams

Ferrari

Minardi

Renault

Toyota

BAR Honda

Jaguar

Jordon

Sauber

Thank you for your time


Problems encountered:There were a number of problems, which occurred in my questionnaire. The first problem was that some people only completed one side of the questionnaire, whilst others did not complete the questionnaire at all.

Another problem, which I encountered with the questionnaire, was that someone did not fill in the questionnaire properly, simply leaving a mark in every single box, whilst another girl ticked one of the boxes which were supposed to contain a rating of one to ten.

The final problem I encountered was that for some reason the secondary data of the list of names from year eleven contained three students from year 12, which I did not notice until after I had handed out the questionnaire but I was unaffected by this. I encountered another error with this list as well because at first I did not notice that the list started on the right hand side but I soon solved this problem by re numbering the data.

I did not encounter any problems with the secondary data from the official formula one website.



Year 10 Statistics Coursework 2004Questionnaire results

Below is the results of my questionnaire for the year seven girls:

Name Form Sex YearQuestion

1Question

2Question 3 Question 4

Question 5

Question 6Rating for

BAR Honda

Rating for

Ferrari

Rating for

Jaguar

Rating for Jordon

Rating for McLaren

Rating for

Minardi

Rating for Renault

Rating for

Sauber

Rating for Toyota

Rating for

Williams

Bird, Jeremia ABR F 7 Yes No No None None 0 0 0 0 0 0 0 0 0 0

Brunning, Abigail MBT F 7 Yes No Yes Ferrari My parents support them

Yes 5 1 2 8 6 9 4 7 3 10

Clifford, Shauna MR F 7 No No No None None 0 0 0 0 0 0 0 0 0 0

Cood, Nicole CO F 7 No No No None None No 0 0 0 0 0 0 0 0 0 0

Harrington, Amy MR F 7 No No No None None 0 0 0 0 0 0 0 0 0 0

Hood, Lisa ABR F 7 Yes No Yes Ferrari Their success Yes 10 1 10 7 1 9 8 8 5 2

Humphries, Jessie CO F 7 No No No None 0 0 0 0 0 0 0 0 0 0

Hyett, Rebecca ABR F 7 Yes No Yes Ferrari None 0 0 0 0 0 0 0 0 0 0

Jeffrey, Stacey RPR F 7 No No No None 0 0 0 0 0 0 0 0 0 0

Jeffs, Sarah MR F 7 No No No None None 0 0 0 0 0 0 0 0 0 0

Letham, Chelsea MR F 7 No No Yes Jaguar My friends support them

Yes 10 3 1 8 2 5 7 9 6 4

Maloney, Katie MR F 7 No No Yes Ferrari It's the only team I hear about

Yes 10 1 4 6 3 9 5 8 7 2

Manfredi, Marianne AKE F 7 No No No None None 0 0 0 0 0 0 0 0 0 0


1Question


Question 5

Question 6Rating for

BAR Honda

Rating for

Ferrari

Rating for

Jaguar

Rating for Jordon

Rating for McLaren

Rating for

Minardi

Rating for Renault

Rating for

Sauber

Rating for Toyota

Rating for

Williams

Mayhew, Jolene MBT F 7 No No No None None 0 0 0 0 0 0 0 0 0 0

McGrouther, Connie AKE F 7 Yes No Yes Ferrari I like the cars Yes 0 0 0 0 0 0 0 0 0 0

Mills, Laura CO F 7 No No No None None 0 0 0 0 0 0 0 0 0 0

Minton, Melissa ABR F 7 Yes No Yes BAR Honda I like the driver(s) Yes 10 5 9 4 1 6 8 3 7 2

Mortlock, Hannah CO F 7 Yes No No None None 0 2 1 0 0 0 0 0 0 0

Morys, Amanda MBT F 7 0 0 0 0 0 0 0 0 0 0

Murphy, Anna AKE F 7 No No No None None 0 0 0 0 0 0 0 0 0 0

Nunn, Abigail MH F 7 No No Yes Jaguar My parents support them

0 0 0 0 0 0 0 0 0 0

Peters, Kimberly AKE F 7 No No No None None 0 0 0 0 0 0 0 0 0 0

Skipp, April MBT F 7 No No No None None 0 0 0 0 0 0 0 0 0 0

Taylor, Dorothy CO F 7 No No No None None No 0 0 0 0 0 0 0 0 0 0

Below is the results of the questionnaire for year eleven girls:


1Question

2Question

3Question


Rating for BAR

Honda

Rating for

Ferrari

Rating for

Jaguar

Rating for

Jordon

Rating for

McLaren

Rating for

Minardi

Rating for

Renault

Rating for

Sauber

Rating for

Toyota

Rating for

Williams

Ayres, Molly LA F 11 No No No None None 0 0 0 0 0 0 0 0 0 0

Ballard, Lucy SBR F 11 No No No None None 0 0 0 0 0 0 0 0 0 0

Baster, Laura DH F 11 No No No None Yes 0 0 0 0 0 0 0 0 0 0

Buckingham, CMI F 11 0 0 0 0 0 0 0 0 0 0


1Question

2Question

3Question


Rating for BAR

Honda

Rating for

Ferrari

Rating for

Jaguar

Rating for

Jordon

Rating for

McLaren

Rating for

Minardi

Rating for

Renault

Rating for

Sauber

Rating for

Toyota

Rating for

Williams

Laura

Curtis, Gemma PJ F 11 No No No None None 0 0 0 0 0 0 0 0 0 0

Dennis, Kirstie SBR F 11 Yes No No None None 8 1 4 6 2 9 5 10 7 3

Harrison, Laura DD F 11 Yes No Yes McLaren Their success

Yes 6 3 4 2 1 9 8 5 7 10

Holmes, Roxanne SBR F 11 No No No None None 0 0 0 0 0 0 0 0 0 0

Kayley, Kimberly SBR F 11 0 0 0 0 0 0 0 0 0 0

Mackechnie, Kirsty

LA F 11 No No No None None 0 0 0 0 0 0 0 0 0 0

Matthews, Emily DH F 11 0 0 0 0 0 0 0 0 0 0

Pearce, Hannah SBR F 11 Yes No No None None 0 0 0 0 0 0 0 0 0 0

Porter, Rochelle LA F 11 Yes Yes Yes Sauber Their success

Yes 9 3 2 10 4 7 6 1 5 8

Purcell, Lindsey LA F 11 No No No None None No 9 3 2 8 4 6 7 10 1 5

Reeve, Hannah PJ F 11 No No No None None 8 5 3 10 6 2 7 4 9 1

Robson, Ella DD F 11 No No No None None Yes 0 0 0 0 0 0 0 0 0 0

Smith, Lucy DD F 11 0 0 0 0 0 0 0 0 0 0

Spellman, Annie DD F 11 No No No None None 0 0 0 0 0 0 0 0 0 0

Stevens, Hayley SBR F 11 0 0 0 0 0 0 0 0 0 0

Suckling, Abby PJ F 11 No No No None None 0 0 0 0 0 0 0 0 0 0

Sutton, Tanya LA F 11 0 0 0 0 0 0 0 0 0 0

Tinslay, Katherine PJ F 11 Yes Yes Yes Williams I like the driver(s)

Yes 6 2 5 4 3 9 7 10 8 1

Whitbread, Kayley DH F 11 No No No None None 10 7 5 8 2 9 3 1 6 4


1Question

2Question

3Question


Rating for BAR

Honda

Rating for

Ferrari

Rating for

Jaguar

Rating for

Jordon

Rating for

McLaren

Rating for

Minardi

Rating for

Renault

Rating for

Sauber

Rating for

Toyota

Rating for

Williams

Winstanley, Charlotte

SBR F 11 No No No None None 0 0 0 0 0 0 0 0 0 0

Below is the results of the questionnaire for year seven boys:


1Question

2Question

3Question

4Question 5

Question 6

Rating for

BAR Honda

Rating for

Ferrari

Rating for

Jaguar

Rating for

Jordon

Rating for

McLaren

Rating for

Minardi

Rating for

Renault

Rating for

Sauber

Rating for

Toyota

Rating for

Williams

Baker, Jed AKE M 7 Yes No Yes Ferrari None 0 0 0 0 0 0 0 0 0 0

Benjamin, Joshua CO M 7 Yes Yes Yes McLaren None 0 0 0 0 0 0 0 0 0 0

Blackwell, Rowan MBT M 7 Yes No Yes Williams My family own a BMW

Yes 0 2 5 0 1 0 4 0 0 3

Bright, Jack RPR M 7 0 0 0 0 0 0 0 0 0 0

Cooper, Matthew AKE M 7 No No No None None 0 0 0 0 0 0 0 0 0 0

Cornish, Chanelle MBT M 7 Yes No Yes Ferrari My parents support them

Yes 3 1 4 5 8 9 10 7 2 6

Couzens, Adam AKE M 7 Yes No No None None 0 0 0 0 0 0 0 0 0 0

Dawson, Luke MR M 7 Yes No Yes Ferrari I like their cars

Yes 10 1 3 8 2 7 6 9 5 4

Deal, Innes ABR M 7 0 0 0 0 0 0 0 0 0 0

Dyer, Steve CO M 7 Yes No Yes McLaren None 0 0 0 0 0 0 0 0 0 0


1Question

2Question

3Question

4Question 5

Question 6

Rating for

BAR Honda

Rating for

Ferrari

Rating for

Jaguar

Rating for

Jordon

Rating for

McLaren

Rating for

Minardi

Rating for

Renault

Rating for

Sauber

Rating for

Toyota

Rating for

Williams

Edney-Hammond, Haydn ABR M 7 Yes Yes Yes Ferrari Their success Yes 5 1 7 6 2 10 4 8 9 3

Fisher, Samuel AKE M 7 0 0 0 0 0 0 0 0 0 0

Holt, Matthew MH M 7 Yes Yes Yes Ferrari I like the driver(s), Their success

Yes 7 1 5 4 2 10 6 8 9 3

Jacobs, Nathan MBT M 7 No No No None 0 0 0 0 0 0 0 0 0 0

Jolley, Cristopher CO M 7 Yes Yes Yes McLaren I like the driver(s)

Yes 7 1 6 8 2 10 5 9 4 3

Kane, Joseph MR M 7 Yes No Yes Ferrari Their success Yes 7 1 4 3 2 8 9 10 5 6

Knight, Ryan RPR M 7 Yes No Yes Williams None 0 0 0 0 0 0 0 0 0 0

Nagorski, Mark MBT M 7 Yes No Yes Ferrari I like the driver(s)

Yes 8 1 4 9 2 6 5 10 7 3

Onslow, Philip AKE M 7 Yes Yes Yes Toyota I like the driver(s)

Yes 6 9 7 6 8 5 6 6 6 8

Paton, Daniel ABR M 7 Yes No Yes Toyota I like the driver(s)

Yes 5 2 4 10 3 8 7 9 1 6

Pease, Thomas MBT M 7 Yes No Yes Ferrari None 0 0 0 0 0 0 0 0 0 0

Pollard, Jake ME M 7 Yes No Yes Ferrari None 0 0 0 0 0 0 0 0 0 0

Rippingale, Matthew RPR M 7 Yes Yes Yes Ferrari Their success Yes 0 0 0 0 0 0 0 0 0 0

Rowlingson, Thomas ABR M 7 Yes Yes No None None No 5 1 8 10 2 7 4 9 6 3

Scillitoe, Liam ABR M 7 No No No None None 0 0 0 0 0 0 0 0 0 0

Sewell, Tom RPR M 7 Yes No Yes Ferrari My parents support them

Yes 0 1 0 0 0 0 0 10 0 0

Seymour, Robert MH M 7 Yes Yes Yes Ferrari My friends suport them

Yes 8 1 7 6 3 9 5 10 4 2

Shadenyi, Anslem CO M 7 Yes No Yes Ferrari None 0 0 0 0 0 0 0 0 0 0

Shreeve, Kalebh ABR M 7 Ferrari None 0 0 0 0 0 0 0 0 0 0


1Question

2Question

3Question

4Question 5

Question 6

Rating for

BAR Honda

Rating for

Ferrari

Rating for

Jaguar

Rating for

Jordon

Rating for

McLaren

Rating for

Minardi

Rating for

Renault

Rating for

Sauber

Rating for

Toyota

Rating for

Williams

Wells, Robert CO M 7 No No Yes Ferrari I like the driver(s)

No 5 1 6 2 3 10 8 7 9 4

Below are the results of the questionnaire for year eleven boys:


1Question

2Question

3Question

4Question 5

Question 6

Rating for

BAR Honda

Rating for

Ferrari

Rating for

Jaguar

Rating for

Jordon

Rating for

McLaren

Rating for

Minardi

Rating for

Renault

Rating for

Sauber

Rating for

Toyota

Rating for

Williams

Baker, Riki DD M 11 No No No None None Yes 0 0 0 0 0 0 0 0 0 0

Bass, Sean CMI M 11 0 0 0 0 0 0 0 0 0 0

Boreham, Andrew PJ M 11 No No Yes McLaren Their success Yes 4 1 5 8 2 10 6 9 7 3

Briggs, Tristan PJ M 11 No No No None None 0 0 0 0 0 0 0 0 0 0

Carter, Oliver DH M 11 No No No None None 7 1 6 5 3 9 4 10 8 2

Clarke, Christopher PJ M 11 No No Yes Sauber They are so rubbish it is funny

Yes 3 10 5 4 9 2 6 1 8 7

Cood, Gary SBR M 11 Yes Yes Yes Williams I like the driver(s) Yes 5 2 6 7 3 10 4 9 8 1

Corbett, John DD M 11 No No No None None Yes 0 0 0 0 0 0 0 0 0 0

Cotton, Patrick CMI M 11 Yes Yes Yes Ferrari I like the driver(s) Yes 8 1 4 5 2 6 7 9 10 3


1Question

2Question

3Question

4Question 5

Question 6

Rating for

BAR Honda

Rating for

Ferrari

Rating for

Jaguar

Rating for

Jordon

Rating for

McLaren

Rating for

Minardi

Rating for

Renault

Rating for

Sauber

Rating for

Toyota

Rating for

Williams

Crane, Harry PJ M 11 No No No None None 0 0 0 0 0 0 0 0 0 0

Curtis, Jamie DH M 11 No No No None None 0 0 0 0 0 0 0 0 0 0

Gibbs, Roscoe SBR M 11 Yes No Yes Williams None 0 0 0 0 0 0 0 0 0 0

Longcroft, Samuel LA M 11 Yes No Yes Ferrari None 0 0 0 0 0 0 0 0 0 0

McStravick, Sean CMI M 11 Yes Yes Yes Williams My parents support them

Yes 8 3 10 5 2 6 4 9 7 1

Mitchell, Thomas PJ M 11 No No No None None 0 0 0 0 0 0 0 0 0 0

Pauley, Jacob LA M 11 No No No None None No 9 1 3 5 2 8 7 10 6 4

Simonds, Andrew PJ M 11 Yes No No None None Yes 5 10 6 4 8 1 7 3 2 9

Skipper, Ian DD M 11 No No No None None No 5 9 6 7 1 10 4 8 3 2

Turner, Robert PJ M 11 0 0 0 0 0 0 0 0 0 0

Williamson, Matthew DD M 11 Yes No No None None No 8 1 4 5 2 9 6 10 7 3

Wright, Samuel LA M 11 Yes No No None None 0 0 0 0 0 0 0 0 0 0

Year 10 Statistics Coursework 2004Hypothesis 1

If the new point system had been used in previous years the team called Minardi would have done a lot better overall and would be higher up in the league of

cars.

I am going to investigate my first hypothesis by drawing box and whisker diagrams for the results of the 2002 Grand Prix season using the original point system and then drawing box and whisker diagram using the recently introduced point system. I will get the total points achieved by each team at each race and then put them into numerical order so I can establish the upper and lower quartiles as well as the median. This will help me to see if the teams overall performance throughout this year would have improved because I will be able to see the spread of the results, showing me the consistency of the team and also whether the box and whisker diagrams have a positive, negative of evenly distributed skew, if the team went from a negative skew to a positive skew this would certainly demonstrate an improvement.

Firstly I will need to organise the results at each of the races in a table. I will begin by putting the results of the Grand Prix using the original point system into a table.

The table produced can be seen below, it has columns for the upper and lower quartiles and the median. The results highlighted represent the outliers which were established in the data. An outlier is established by doing the following:

To establish the higher outliers I would add 5.25 to the upper quartile, any of the results that come above this value will be considered as outliers. To establish the lower outliers I would take away 5.25 from the lower quartile, any of the results that come below this value will be considered as outliers. An outlier is a value which is unusually high or unusually low compared with the rest of the data.

Pos Team TotalMean

Average L.Q U.Q Median

1 Ferrari 16 13 16 16 16 16 16 14 10 10 4 10 16 10 16 6 16 221 13 10 16 16

2 Williams-BMW 3 10 3 0 6 4 4 0 5 6 16 8 7 6 7 4 3 92 5.41 3 7 5

3 McLaren-Mercedes 4 2 4 0 3 0 5 9 10 4 0 4 1 4 1 10 4 65 5.91 1 4.5 4

4 Renault 1 0 2 5 0 0 0 1 1 0 3 3 2 0 0 3 2 23 2.09 0 2.5 1

5 Sauber-Petronas 0 1 0 0 0 1 0 0 0 0 3 0 0 5 0 0 1 11 1.00 0 1 0

6 Jordon-Honda 2 0 0 0 0 0 1 2 0 0 0 0 0 0 2 2 0 9 0.82 0 1.5 0

7 Jaguar Cosworth 0 0 0 4 1 0 0 0 0 3 0 0 0 0 0 0 0 8 0.73 0 0 0

8 BAR Honda 0 0 1 1 0 5 0 0 0 0 0 0 0 0 0 0 0 7 0.64 0 0 0

9 Minardi-Asiatech 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0.18 0 0 0

10 Toyota 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 2 0.18 0 0 0

11 Arrows Cosworth 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 2 0.18 0 0 0

Below is the results, and the medians, upper quartiles and lower quartiles l new point system (again the outliers are highlighted:

Pos Team TotalMean

Average L.Q U.Q Median

1 Ferrari 18 15 18 18 18 18 18 16 10 10 6 10 18 10 18 10 18 249 14.65 10 18 18

2 Williams-BMW 5 14 5 0 10 7 6 2 9 9 8 18 12 11 8 11 6 141 8.29 5.5 11 8

3 McLaren-Mercedes 6 4 6 2 5 0 9 13 14 6 0 6 3 6 3 10 6 99 9.00 3 7.5 6

4 Renault 3 0 5 9 0 0 1 3 3 0 4 5 5 5 4 0 4 51 4.64 0 5 3

5 Sauber-Petronas 2 5 0 0 0 3 2 0 2 0 7 0 1 9 0 1 5 37 3.36 0 4 1

6 BAR Honda 0 0 3 3 1 9 0 1 0 0 1 0 2 2 0 0 4 26 2.36 0 2.5 1

7 Jordon-Honda 4 1 2 1 0 2 3 4 0 0 0 0 0 0 4 4 0 25 2.27 0 3.5 1

8 Jaguar Cosworth 0 0 0 6 3 0 0 0 0 5 0 3 0 0 0 0 0 17 1.55 0 1.5 0

9 Toyota 1 0 0 0 2 0 0 0 0 3 2 3 0 1 1 0 0 13 1.18 0 1.5 0

10 Minardi-Asiatech 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 6 0.55 0 0 0

11 Arrows Cosworth 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 0 0 6 0.55 0 0 0

I can see that Minardi would have actually been in an even worse position, had the new point system been introduced in 2002. If the new point system had been introduced.

Had the new point system been already been introduced I can see that the constructors positioning between the positions of 6-10 would have been a lot different, this is because there were more occasions for some of the teams to be awarded and they received more points in the new system than in the old system. The first 5 constructors already had a large spread between the points they achieved, in the old point system, and this meant that there would still be a large gap between the points in the new point system.

The new point system enables more drivers to achieve points because it allows and extra two drivers to be awarded points compared with the old system. It also is more evenly spread out, which can be seen below

Old point system:

Place Points awarded1st 102nd 63rd 44th 35th 26th 1

New point system:Place Points awarded1st 102nd 83rd 64th 55th 46th 3

7th 28th 1

In the old point system there was a four-point gap between first and second place, whereas in the new point system there is only a two point gap. Lowering this gap enabled the Formula One Officials to award a further two places points i.e. 7th and 8th position can now achieve points. There is a possibility that they changed the results in order to award consistency. I can examine consistency using box and whisker diagrams.

On the following pages I will draw two box and whisker diagrams for each team, one for their results using the old point system and one for the results using the old system. To help me compare the two I will place them one on top of the other.

Drawing box and whisker diagrams will enable me to assess each teams results depending on consistency because I will be able to see the skew of the data as well as the spread of the data.

Year 10 Statistics Coursework 2004Hypothesis 1 – Analysis of Box and Whisker Diagrams

Ferrari:In the box and whisker diagram for the team called Ferrari, using the original point system there is a large positive skew, this was because the median and upper quartile were the same value. The reason behind why they were the same value is that the majority of the results were Ferrari were high, and in some cases at the maximum point score. I decided to indicate where the outlier was but to leave it in because that meant that the diagram would still have a whisker. This outlier occurred because in this instance only one Ferrari car achieved points, usually both cars achieve a high score. The box and whisker diagram shows that Ferrari are a very successful team, however because of the spread of the data it also shows that they are not as consistent as some other teams.

In the box and whisker diagram which shows the results for Ferrari using the new point system there is an even larger positive skew, again the upper quartile and median were the same value because the majority of the results are high and in some cases at the maximum point score. In this diagram there were no outliers. There is only one whisker because the upper quartile and median were at the maximum score. There is a larger spread between the data than there was using the original point system, which again indicates some inconsistency.

The two diagrams show me that the team Ferrari would have done even better had the new point system been introduced in 2002. This is also demonstrating in the tables, I can see that there would, however, be a reduction in the spread between Ferrari and the team in second place. The diagrams also show that there is a large spread in the points for the team Ferrari.

Williams BMW:The box and whisker diagram for Williams BMW using the original point system is evenly distributed, this represents a consistency for this team, however this is only achieved if I do not take into account the outlier. Williams BMW tend to achieved in the lower point range but overall they were second. Although they achieved points mainly in the lower range they were consistent in doing so, it therefore can be argued that Williams BMW were in fact more successful in 2002.

The box and whisker diagram for Williams BMW using the new point system has a positive skew and there was an outlier, when they achieved zero points. This shows that there was a slight inconsistency in the points scored. This shows me that Williams BMW would have actually benefited better using the original point system because although they would not have achieved more points, and be closer in total points to the team Ferrari, they would have been more consistent. There is a smaller spread for the results of Williams BMW, compared with Ferrari.

McLaren Mercedes:Using the original point system the box and whisker diagram for the team McLaren has a negative skew. The spread of the data is a lot smaller than the spread of the data

for the team Ferrari, which suggests more of a consistency but as there is a negative skew they were not as consistent as Williams BMW. There was only one outlier in the results, which was at ten points. IT was an outlier because McLaren Mercedes tend to score in the lower point range. There were few instances where McLaren achieved zero points.

The box and whisker diagram using the new point system still has a negative skew, in this instance there were two outliers when they scored unusually high numbers of points. There is a slightly larger spread of data with the new point system. The would benefit from the new point system because there were few occasions in which they achieved zero points, meaning that the lower quartile upper quartile and median were higher.

The box and whisker diagrams show that McLaren Mercedes would have benefited more from the new point system because this would increase the number of points scored as well as their consistency. However the new point system would mean that there would be an even larger spread between their results and the results of the second place team Williams.

Renault:The box and whisker diagram for the team named Renault using the box and whisker diagram has a slight positive skew. There is only one whisker because the lower quartile was at zero points. This team seems fairly consistent, despite mainly achieving low points and sometimes no points at all. As the upper quartile was quite a small value and the lower quartile was the minimal value there were no outliers in the results. There is only a small spread between the points scored for Renault, a lot lower compared with Ferrari. This indicates a degree of consistency for this team. There is only one whisker in both diagrams because in both cases the lower quartile was zero.

The results for Renault using the new point system have a negative skew; the skew of the data is larger than the skew with the original point system. This shows that with the new point system they would be less consistent. However they would achieve more points overall. With the new point system there would be a larger spread between the total points Renault and the second third place team McLaren. Renault would still be in the same position as they were with the original point system as they would be in the old system (i.e. they would still be in fourth place). The diagrams show me that Renault would benefit more with the old point system because although they would have more points, there would be a larger gap between them and the team above them and they would also be less consistent.

Sauber Petronas:In the box and whisker diagram which represents the scores for the team called Sauber Petronas, using the original point system, the lower quartile and median are at the same value, which resulted in a positive skew. This diagram shows that Sauber often score zero points or very low points, though there was one instance in which they achieved a total of five points. This shows that although there results are low, they are fairly consistent, despite the slight positive skew. There is a very small spread in the data because of the tendency to score low points, if any at all.

The box and whisker diagram using the new point system has a larger spread and more of a positive skew to it, this is because the lower quartile and median would be different values. I can see from this diagram that Sauber would benefit slightly from the new points system because it would enable them to achieve more points more often, however it would mean that there consistency would not be as good. The diagrams only have one whisker because there were many instances where Sauber-Petronas achieved zero points, due to either not getting high enough in position or retirement of the cars.

Sauber-Petronas would still be fifth over all, so they would not benefit in that sense. The new point system would mean that there would be a larger spread between the points achieved by Sauber-Petronas and the fourth place team Renault. However the gap would only increase by two points. It would appear that they would be slightly more benefited by the original point system but the new point system does mean they would achieve more points more often.

BAR Honda:The box and whisker diagram for BAR Honda using the original point system has the lower and upper quartiles as well as the upper quartile all at zero, this was because of frequent scoring of zero points due to retirement or not being high enough in position to achieve any points. When a diagram was drawn using the old point system the lower quartile, upper quartile and median were all at different values, which would be a clear improvement. The new diagram has a slight positive skew and one outlier, where the team achieved an unusually high number of points.

By looking at the results tables it is possible to see just how beneficial the new point system would have been to BAR Honda because they would have achieved a two places higher, i.e. from eight to sixth. The new point system would have given BAR Honda far more opportunities to score points.

Jordan:The box and whisker diagram fro the team named Jordan, using the original point system, has the lower quartile and median both at the same value of zero. This resulted in a positive skew. The reason the lower quartile and median were at the same value is that there were many instances where Jordan scored zero points due to not achieving a high enough position or because of retirement. There were no outliers for Jordan because they rarely scored a high number of points. There is only a small spread in the data.

The box and whisker diagram for their results using the new point system has the lower quartile and median at different values, it also has a larger spread. There would also be a larger positive skew because of there being more instances where they scored higher points.

From the tables of results I can see that Jordan would not have benefited from the new point system as because of BAR Honda would be more successful, it would mean they would go down a position.

Jaguar:The team Jaguar had an upper and lower quartile as well as a median at the same value of zero because of these being so low; it meant that there were no outliers in the results. The three elements were so low because of the team frequently scoring zero points due to not achieving a high enough position as well as retirements.

The box and whisker diagram using the new point system has a larger spread in the data because the upper quartile is a different value to the lower quartile, which results in a positive skew, this shows a benefit to the team. As the quartiles were such low values it meant that there were no outliers in the results.

I can see from the table of results, that the new point system would be a slight benefit to the team Jaguar because it would mean that this constructor would be one position higher.

Toyota:Again, for this team the lower and upper quartiles as well as the median are all at zero, this results in an extremely small spread of the data and also meant that there were no outliers. The diagram shows us that this team were consistently scoring zero points due to not achieving high enough points and retirements

From the box and whisker diagram they would have if the new point system was enforced in the year, there is a larger spread in the data because the upper quartile is slightly higher than the lower quartile and median. However it is notable that the lower quartile and median would still be at zero. There is a positive skew in the data, and there are no outliers. I can see from the diagrams that Toyota would have benefited slightly from the new point system and that there would be a larger spread of results.

From the results table I can also see the slight benefit they would have had, had the new point system been introduced at an earlier year because overall they would be one place higher, from tenth place to ninth place, which would be because of their being more instances where they scored higher points.

Minardi Asiatech:Minardi Asiatech frequently scored zero points in 2002, in fact there was only one race in which they scored points. There were so many occurrences of nil points because they are only a low budget team, resulting in many retirements and not achieving places in which point are awarded. This meant that the lower quartile and the upper quartile and the median were at the same minimal value of zero. There is only a spread of two between their points, and the interquartile range is zero.

The box and whisker diagram using the new pint system has very little improvement the two quartiles and the median are still at zero, this is because of they would still constantly achieve no points in races. There would still be only one occasion in which Minardi would score and there would still be a larger hap from the higher achieving constructor above them, this would mean that Minardi would not really benefit from the new point system and would not be higher up in the league of cars. This means that my hypothesis was incorrect.

Arrows Cosworth:Arrows Cosworth are in the same situation as Minardi. Arrows Cosworth frequently scored zero points in 2002, in fact there was only two races in which they scored points and in these races they only achieved one point in total. There were so many occurrences of nil points because they are only a low budget team, resulting in many retirements and not achieving places in which point are awarded. This meant that the lower quartile and the upper quartile and the median were at the same minimal value of zero. There is only a spread of two between their points, and the interquartile range is zero.

The box and whisker diagram using the new pint system has very little improvement the two quartiles and the median are still at zero, this is because of they would still constantly achieve no points in races. The whisker is ever so slightly longer, but incorporates an outlier, which I decided to leave in to make the diagram slightly more graphical. There would still be only two occasions in which Minardi would score and they would still have the same points as Minardi, this would mean that Arrows Cosworth would not really benefit from the new point system.

Conclusion for hypothesis one:In conclusion I can see that my hypothesis that the team Minardi-Asiatech would have done better had the new point system been introduced in an earlier year was incorrect. This team would still be a low scoring team, at the bottom of the league of constructors. As the team are low budget compared with teams like Ferrari it is difficult for them to achieve points because they cannot keep up with the much faster and better performing cars made by the higher budgeted teams. Minardi constantly retire, whereas there are few occasions in which Ferrari retire because this team has a better performing car because they can afford to put a lot more money on it and they can also afford to higher better drivers.

There would be quite a difference in the positioning of the cars achieving the positions in the league of constructors between 5-8, which suggest that the formula one officials felt that it was necessary to award consistency as well as positioning in the races because there are more opportunities to score points with the new point system compared with the old system and it is more evenly spread out.

Year 10 Statistics Coursework 2004Hypothesis 2 – Comparative Pie charts

If I draw a comparative pie chart for the favoured teams of each of the four groups (ie year seven girls, year seven boys, year eleven girls and year eleven boys) I will be able to compare their choices.

I will use the year seven girls in order to get the radii for the other groups.

Year seven girls:I have decided to use a radius of 2cm for the year seven girls in order to be able to draw the three other pie charts.

The are of the pie chart will be:

Π x 2cm2 = 12.57cm2 (4 s.f.)

I now need to calculate what the are will be for one person, there are 25 year seven girls so I will need to divide the area by 25, as can be seen below:

12.57 / 25 = 0.5027cm

I will now be able to work out the angles for each of the teams in the normal way. I will begin by working out what angle represents one person as follows:

360 / 25 = 14.4°

I can now calculate the angles for each team:

None: 14.4 x 17 = 244.8°BAR Honda: 14.4 x 1 = 14.4°Ferrari: 14.4 x 5 = 72°Jaguar: 14.4 x 2 = 28.8°

Year seven boys:For the year seven boys, firstly I need to work out the radius required to draw the pie chart. To do this I will need to use the area for one person calculated in the year seven girls. As follows:

0.5027 x 30 =15.081Πr2 = 15.081r2 = 15.081 / Πr = 2.2 cm (3 s.f.)

Again I can now calculate the angles for each team in the normal way, firstly by working out the angle for one person.

360 / 30 = 12°

I can now use this value to calculate the angles for each team:

None: 12 x 8 = 96°Ferrari: 12 x 15 = 180°McLaren: 12 x 3 = 36°Toyota: 12 x 2 = 24°Williams: 12 x 2 = 24°

Year eleven girls:

The radius for the year eleven girls will be as follows:

0.5027 x 24 = 12.0648Πr2 = 12.0648r2 = 12.0648 / Πr = 1.96 cm (3 s.f.)

I now need to calculate the angle for one person:

360 / 24 = 15cm2


None: 15 x 21 = 315°McLaren: 15 x 1 = 15°Sauber: 15 x 1 = 15°Williams: 15 x 1 = 15°

Year eleven boys:

The radius for the year eleven girls will be as follows:

0.5027 x 21 = 10.5567Πr2 = 10.5567r2 = 10.5567 / Πr = 1.83 cm (3 s.f.)

I now need to calculate the angle for one person:

360 / 24 = 15cm2


None: 15 x 21 = 315°McLaren: 15 x 1 = 15°Sauber: 15 x 1 = 15°Williams: 15 x 1 = 15°

I am now able to draw a pie chart for each grouping, the comparative pie charts can be seen below.

Year seven girls:

None

Ferrari

BAR Honda

Jaguar

Year seven boys:

None

Ferrari

McLaren

Toyota

Williams BMW

Year eleven girls:

None

McLaren

Sauber

Williams BMW

Year eleven boys:

None

Ferrari

McLaren

Sauber

Year 10 Statistics Coursework 2004Analysis of Comparative Pie Charts

Williams BMW

The year seven girls pie chart has a predominance of people not having a favourite team, this may be because females are not as into car racing as males are and therefore would not watch formula one in order to have a favourite team. I can see that the next popular selection of favourite team was Ferrari. Last year the team Ferrari won the constructors cup and their driver Michael Schumacher also won the drivers cup and this may mean that these people have Ferrari as their favourite team because of the successes of this team. In the questionnaire I can see that one person supported Ferrari because of their success and another supported them because it was the only team they had ever heard about, which suggest that my hypothesis of the more successful the team the more popular they are.

The pie chart representing the year seven boys has a larger area compared with the other pie charts because this was the group I had to hand out the most questionnaires to. The predominately favoured team for this group of people is clearly Ferrari, at total of 50% of year seven boys chose this for a favourite team. It is interesting to note that only four of these people said the supported them for their success, however this may have been more because some of the year seven boys only filled in half of the questionnaire. This pie chart slightly agrees with my hypothesis. Williams-BMW came second last year, it is interesting that Williams are joint fourth most favoured for year seven boys, after the team McLaren (who came third last year). None of the people who favoured McLaren did so because of their success, which is the same with Williams-BMW.

There is a very large area in the year eleven girls pie chart that do not have a favourite team, perhaps when I selected the data in un-intentionally had skewed data in which I chose predominately people who did not support anyone within the group of year eleven girls. It is notable that their were absolutely zero year eleven girls who support the team Ferrari, which would slightly disprove my hypothesis. There were only two girls who supported the team they supported because of their success, one supported McLaren the other Sauber. Overall, last year Sauber achieved fifth place, about half way through all of the constructors, which suggests my hypothesis is correct. McLaren came third, which again suggests my hypothesis was correct. The person who supported the second place team Williams-BMW did so because the liked the drivers, which does not go with my hypothesis.

The pie chart for year eleven boys has the smallest are because I asked the fewest amount of people in year eleven boys. Most of the these people did not support a team. The team which was most supported by this group was Williams-BMW who came second last year in the constructors cup, however the people who supported Williams did not do so because of the success of the team, suggesting my hypothesis as incorrect. The second most favoured team was Ferrari, but neither of the two people supported them because of their success, one of them may have done but they only filled in one side of the questionnaire so it is difficult to say whether this helps to either prove or disprove my hypothesis.

I can see that some of the results achieved did fit with my hypothesis, however there were only seven people who admitted to supporting the team because of their success, this figure may have been larger if more people had filled in both sides of the questionnaire.

In order to see more accurately whether my hypothesis is correct I am going to use Spearman’s Rank Coefficient.

Year 10 Statistics Coursework 2004Hypothesis 2 – Spearman’s Rank Coefficient

Below is a table which will help me to calculate the spearman’s rank coefficient using the results of the entire population questioned and the results of the 2003 Grand Prix season.

Spearman’s rank is calculated using the following equation:

P= 6Σd 2 n(n-1)

I will now need to insert the appropriate numbers in order to calculate spearman’s rank. This is the

calculation I will do:

P= 6 x 46 10(10-1)

P = 276 990 P = 0.72

The spearman’s rank coefficient for these results is 0.72(to 2 d.p.) and this shows that there is a weak positive correlation between the popularity of the team and their success. I suspect there will be a better correlation between the success of the team compared with the regular viewers using the results of the 2003 Grand Prix season.

Spearman’s rank is calculated using the following equation:

P= 6Σd 2 n(n-1)

I will now need to insert the appropriate numbers in order to calculate spearman’s rank. This is the

calculation I will do:

P= 6 x 28 10(10-1)

Team Position Rank d d2

BAR Honda 5 8 -3 9Ferrari 1 1 0 0Jaguar 7 7 0 0Jordon 9 6 3 9McLaren 3 2 1 1Minardi 10 9 1 1Renault 4 4 0 0Sauber 6 10 -4 16Toyota 8 5 3 9Williams 2 3 -1 1 Total 46

Team Position Rank d d2

BAR Honda 5 7 -2 4Ferrari 1 1 0 0Jaguar 7 5 2 4Jordon 9 6 3 9McLaren 3 2 1 1Minardi 10 10 0 0Renault 4 4 0 0Sauber 6 9 -3 9Toyota 8 8 0 0Williams 2 3 -1 1 Total 28

P = 168 990 P = 0.83

The spearman’s rank coefficient for these results is 0.83(to 2 d.p.) and this shows that there is a fairly strong positive correlation between the popularity of the team and their success using the results of the 2003 Grand Prix season and the overall ranking for the teams using the results obtained from regular viewers. I suspect there is a better correlation between these results because regular viewers will have a complete understanding of the sport.

I could also present these results graphically, which I have done in the following graphs. I can see that there is a slightly better correlation between the graph showing the results with the regular viewers, as was suggested in the Spearman’s Rank Coefficient.

The results of the Spearman’s Rank Coefficient and the scatter graphs showed that there is a weak correlation between the success of team and their popularity, I can see that there is a significant improvement of the correlation of success and popularity with the regular viewers of formula one. This is probably because they have a far better understanding of the sport meaning that they would be more slightly more likely to support the more successful teams. The Spearman’s Rank Coefficient shows that my hypothesis of the more successful the team are the more popular they are is to some extent correct because of their being a weak correlation between the overall ranking of the teams and the position in the year of the teams, meaning there is a correlation between the success and the popularity. The trouble is I do not have sufficient evidence or a strong enough correlation to prove that my hypothesis is correct.

Year 10 Statistics Coursework 2004Hypothesis 3

In order to prove or disprove this Hypothesis I will take the average position for all of the races, excluding the race at the home ground at then see whether they were above average in their home track.

Below are the results for the McLaren Mercedes driver named David Coultard. He has a British nationality. The total represents the total of the positions they achieved and the mean average represents the mean position they achieved.

Grand Prix Date Team Grid Race Pos Points Total Australian 09/03/03McLaren-Mercedes 11 1 10 10 Malaysian 23/03/03McLaren-Mercedes 4 Ret 0 10 Brazilian 06/04/03McLaren-Mercedes 2 4 5 15 San Marino 20/04/03McLaren-Mercedes 12 5 4 19 Spanish 04/05/03McLaren-Mercedes 8 Ret 0 19 Austrian 18/05/03McLaren-Mercedes 14 5 4 23 Monaco 01/06/03McLaren-Mercedes 6 7 2 25 Canadian 15/06/03McLaren-Mercedes 11 Ret 0 25 European 29/06/03McLaren-Mercedes 9 15 0 25 French 06/07/03McLaren-Mercedes 5 5 4 29 German 03/08/03McLaren-Mercedes 10 2 8 41 Hungarian 24/08/03McLaren-Mercedes 9 5 4 45 Italian 14/09/03McLaren-Mercedes 8 Ret 0 45 United States 28/09/03McLaren-Mercedes 8 Ret 0 45 Japanese 12/10/03McLaren-Mercedes 7 3 6 51

Total 52 Mean Average 4 British 20/07/03McLaren-Mercedes 12 5 4

I can see that at the British Grand Prix David Coultard achieved an average score, this does not agree with my hypothesis that drivers tend to do better at their home track.

Below are the results for the Ferrari driver named Michael Schumacher. He has a German nationality, which will mean I will need to see whether he does better than average on the German grand prix.

Grand Prix Date Team Grid Race Pos Points Total Australian 09/03/03Ferrari 1 4 5 5 Malaysian 23/03/03Ferrari 3 6 3 8 Brazilian 06/04/03Ferrari 7 Ret 0 8 San Marino 20/04/03Ferrari 1 1 10 18 Spanish 04/05/03Ferrari 1 1 10 28 Austrian 18/05/03Ferrari 1 1 10 38 Monaco 01/06/03Ferrari 5 3 6 44 Canadian 15/06/03Ferrari 3 1 10 54 European 29/06/03Ferrari 2 5 4 58 French 06/07/03Ferrari 3 3 6 64 British 20/07/03Ferrari 5 4 5 69 Hungarian 24/08/03Ferrari 8 8 1 72 Italian 14/09/03Ferrari 1 1 10 82 United States 28/09/03Ferrari 7 1 10 92 Japanese 12/10/03Ferrari 14 8 1 93 Total 47Mean Average 3 German 03/08/03Ferrari 6 7 2 71

I can see from this table that Michael Schumacher did not achieve a higher that average position at the German grand prix, which does not agree with my hypothesis.

Below are the results for Jenson Button, who has a British Nationality, I will need to see if his performance at the British Grand Prix was better than average.

Jenson Button 2003

Grand Prix Date Team Grid Race Pos Points Total Australian 09/03/03BAR-Honda 8 10 0 0 Malaysian 23/03/03BAR-Honda 9 7 2 2 Brazilian 06/04/03BAR-Honda 11 Ret 0 2 San Marino 20/04/03BAR-Honda 9 8 1 3 Spanish 04/05/03BAR-Honda 5 9 0 3 Austrian 18/05/03BAR-Honda 7 4 5 8 Canadian 15/06/03BAR-Honda 17 Ret 0 8 European 29/06/03BAR-Honda 12 7 2 10 French 06/07/03BAR-Honda 14 Ret 0 10 German 03/08/03BAR-Honda 17 8 1 12 Hungarian 24/08/03BAR-Honda 14 10 0 12 Italian 14/09/03BAR-Honda 7 Ret 0 12 United States 28/09/03BAR-Honda 11 Ret 0 12 Japanese 12/10/03BAR-Honda 9 4 5 17 Total 67Mean Average 5 British 20/07/03BAR-Honda 20 8 1 11

I can see that Jenson Button did not achieve better points on average in the British Grand Prix, he achieved three positions below average. This further proves that my Hypothesis was incorrect. I will now examine some more drivers to see if they agree with hypothesis I made at the beginning of the investigation.

Christiano da Matta is a Brazilian nationality driver for the team Toyota, if my hypothesis is correct in theory he should perform better than average on the Brazilian Grand Prix.

Cristiano da Matta 2003

Grand Prix Date Team Grid Race Pos Points Total

Australian 09/03/03Toyota 16 Ret 0 0

Malaysian 23/03/03Toyota 11 11 0 0

San Marino 20/04/03Toyota 13 12 0 0

Spanish 04/05/03Toyota 13 6 3 3

Austrian 18/05/03Toyota 13 10 0 3

Monaco 01/06/03Toyota 10 9 0 3

Canadian 15/06/03Toyota 9 11 0 3

European 29/06/03Toyota 10 Ret 0 3

French 06/07/03Toyota 13 11 0 3

British 20/07/03Toyota 6 7 2 5

German 03/08/03Toyota 9 6 3 8

Hungarian 24/08/03Toyota 15 11 0 8

Italian 14/09/03Toyota 12 Ret 0 8

United States 28/09/03Toyota 9 9 0 8

Japanese 12/10/03Toyota 3 7 2 10 Total 110Mean Average 8 Brazilian 06/04/03Toyota 18 10 0 0

The table I have produced again appears to disprove my hypothesis further.

It seems that there is sufficient evidence to say that my hypothesis of the drivers performing better at their home ground is incorrect because in the examples above the drivers achieved a position either below average or average. In conclusion their appears to be no significant improvement at races at the drivers home track, which may suggest that the drivers treat it as any other race. Perhaps drivers do worse compared with the average position because there is an increased pressure to perform well.

Year 10 Statistics Coursework 2004Overall Conclusion

In conclusion I have seen that only my second hypothesis was correct, and this did not have sufficient evidence to be completely proved. Perhaps if the new point system

was introduced in 2002 there would be a slightly better correlation, or even a slightly worse but it is not possible to say whether this was correct simply because this was not the case, so peoples opinions cannot be affected by this.

The box and whisker diagrams demonstrated a range of different things; I saw that with the old system the most successful team constancy wise was Williams BMW because excluding the outlier their diagram was very evenly distributed. Perhaps the formula one officials took into consideration that it is important to award consistency as well as positioning by having less spread out points given at each position and giving more opportunities for drivers to achieve points.

My third and final hypothesis that drivers perform better at their home track was incorrect, I thought that they may have a better performance at this track because of an increased determination to win, however I have seen that in the examples I used the drivers did worse than average. There may also be a possibility that they did worse than average because of their being so much pressure on them to perform well but this is not possible to say.

There is a possibility that the people I selected for the year eleven girls were slightly skewed because the majority of them did not support a team, this would suggest some in-effectiveness in my investigation. The overall effectiveness of my investigation was not excellent, this was because I encountered many problems involving my questionnaire, such as receiving back un-answered and half answered questionnaire, problems with the lists I was given and some people not filling in the questionnaire properly. However I think it was inevitable to come across such problems, and this is what limits any statistical investigation. This is why statistics may sometimes go to the people personally to get them to fill in the questionnaire, which was not possible for me to do so. Perhaps if I chose another sample of people my hypothesis that the success of a team correlates with the popularity would have been better proved or disproved. The sample I chose was supposed to represent a certain population of people i.e. year sevens and year elevens and there is quite a large possibility that I have not effectively done so. There may have been un-intentional skews in the data but this would not have been done on purpose because I selected the people randomly.

Overall it would seem that my investigation was an effective one. However in the end I only needed to use the results for the 2002 and the 2003 Grand Prix seasons and this means that my planning was not completely successful. I found it fairly difficult to select the correct graphs and appropriate statistical calculations to help me to either prove or disprove my hypothesises.

Documents

Year 10 Statistics Coursework 2004