First Draft of Math IA

8/12/2019 First Draft of Math IA

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Contents

Statement of Intent.........................................................................3

Raw Data...........................................................................................4-17

Calculation........................................................................................19-22

Error test (Graph) .............................................................................................22-25

Conclusion...........................................................................................25

Bibliography.........................................................................................26


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3

Statement of Intent

My aim is to find correlation between racers income and racers average performance. In any occupation someones achievementusually will affect their

salary. Salary can be seen as a reward and incentive to get a better achievement in a job. I want to test the correlation between the racers achievement

and the salary they received. To test this hypothesis I will calculate the chi squared test of the data.

I found the income per race by dividing the income by the number of races that the driver took which also leads to their average rank. It can also relate to

the experience of the driver by dividing the income by the period of time that they have been racing in the group. It indicates to find out the mean on this

data. As my prediction, since there is a difference between from annual income and income from per race, I will find a line of best fit from which I can

predict from the result.


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4

Race1 Race2Race

3Race4 Race 5

Race

6Race7 Race8 Race9

Race

10

Race

11

Race

12

Rac

e

13

Race

14

Race

15

Race

16

Race

17

Race

18

Race

19

Rac

e

20

Race

21

Allgaier,

Justin 2 1 2 30 27 21 4 5 37 1 3 2 1 8 6 16 4 4 1 1 1

Armstrong

Caleb Race1 Race2 Race3 Race4 Race5

6 55 15 20 55

Armstrong

Dakoda Race1 Race2 Race3 Race4 Race5 Race6

20 14 8 8 1 4

Arpin steve Race1 Race2

12 30

Baird Bill Race1 Race2 31,5

36 27

Basham

Darrell Race1 Race2 Race3 Race4 Race5 Race6t Race7 Race8 Race9 Race10 Race11

Race1

2

Rac

e1

3

Race1

4

Race1

5

Race1

6

Race1

7

Race

18 Race19

27 35 17 23 35 19 24 28 14 23 22 28 21 28 18 21 25 17 36

Benjamin

Kyle Race1 Race2 Race3 Race4 Race5 Race6 Race7 Race8

2 11 23 7 8 1 5 1

Berte Tom Race1 Race2 Race3 Race4

17 26 24 18


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5

Blackburn

Steve Race1 Race2

4 5

Blaney Ryan Race1 Race2 Race3

2 5 3

Blankenship

John Race1 Race2

15 6

Boat Chad Race1

7

Boston Justin Race1 Race2 Race3 Race4 Race5 Race6 Race7 Race8 Race9 Race10 Race11

Race1

2

Rac

e1

3

Race1

4

Race1

5

Race1

6

Race1

7

Race

18 Race19

Rac

e2

0

Race2

1

31 6 9 30 4 4 9 4 8 18 7 6 3 6 5 2 3 16 23 8 5

Bourque

Pierre Race1

15

Bowen

Anderson Race1 Race2 Race3

3 20 15

Bowman Alex Race1 Race2 Race3 Race4 Race5 Race6 Race7 Race8 Race9 Race10 Race11

Race1

2

Rac

e1

3

Race1

4

Race1

5

Race1

6

Race1

7

Race

18 Race19

30 3 1 32 9 11 3 2 1 13 1 8 22 3 13 2 2 5 1

Brent Robb Race1 Race2

11 8


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6

Brevak Brent Race1 Race2 Race3 Race4 Race5 Race6

38 26 9 39 25 33

Buescher

Chris Race1 Race2 Race3 Race4

30 1 22 18

Buescher

James Race1 Race2 Race3 Race4

4 18 30

Bujdoso

Robert Race1 Race2 Race3 Race4 Race5 Race6

12 18 15 13 7 5

Canache

Nelson Race1 Race2 Race3 Race4 Race5 Race6 Race7 Race8 Race9 Race10 Race11

Race1

2

Rac

e1

3

Race1

4

Race1

5

Race1

6

Race1

7

Race

18 Race19

22 22 33 27 16 16 14 32 19 12 30 7 14 10 12 23 12 11 12

Carter Roger Race1 Race2 Race3 Race4 Race5 Race6 Race7

35 32 34 31 31 33 33

Charlson

Drew Race1 Race2 Race3

2 41 18

ChastainBenny Race1 Race2 Race3 Race4 Race5 Race6 Race7 Race8 Race9

35 27 16 24 25 33 41 28 31

Corr Sean Race1 Race2 Race3 Race4 Race5

43 14 30 30 12


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7

Coulter Joey Race1 Race2 Race3

40 14 9

Cox Ron Race1 Race2

22 12

Cross Brent Race1 Race2

20 25

Cushman

George Race1 Race2 Race3 Race4

5 8 14 32

Dillon Ty Race1 Race2 Race3 Race4 Race5 Race6 Race7 Race8 Race9 Race10 Race11

Race1

2

Rac

e

13

Race

14

Race1

5

Race

16

Race1

7

Race

18 Race19

11 1 2 1 8 1 4 1 4 11 1 1 1 1 13 4 2 8 7

Dufault

Maryeve Race1 Race2 Race3

26 23 19

Duno Milka Race1 Race2 Race3 Race4 Race5 Race6 Race7 Race8 Race9 Race10 Race11

Race1

2

Rac

e

13

37 18 31 37 24 10 16 18 17 19 17 13 33

Elliot Chase Race1 Race2 Race3 Race4

24 26 27 13

Enfinger

Grant Race1 Race2 Race3 Race4 Race5 Race6

13 3 2 27 8 3


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Evans Jr.

Charles Race1 Race2 Race3 Race4 Race5

16 34 23 11 7

Ferns Taylor Race1 Race2 Race3 Race4 Race5 Race6 Race7 Race8

9 20 12 15 9 10 13 12

Fike AJ Race1

24

Finley Chad Race1 Race2 Race3 Race4 Race5 Race6

11 3 7 23 30 2

Fowler Kyle Race1 Race2 Race3 Race4 Race5

16 36 23 24 27

Fox Steve Race1 Race2 Race3

15 29 23

Gale Cale Race1 Race2

13 1

Gallagher

Spencer Race1 Race2 Race3 Race4 Race5 Race6 Race7 Race8 Race9 Race10 Race11

Race1

2

Rac

e1

3

Race1

4

Race1

5

Race1

6

Race1

7

Race

18 Race19

Rac

e2

0

Race2

1

21 22 2 27 26 8 8 17 13 16 5 11 2 4 14 16 3 7 5 4

George, Jr.

Tim Race1 Race2 Race3 Race4 Race5 Race6 Race7 Race8 Race9 Race10 Race11

Race1

2

Rac

e1

3

Race1

4

Race1

5

Race1

6

Race1

7

Race

18 Race19

27 18 11 4 4 32 1 3 11 2 5 28 2 16 9 9 3 16 17


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9

Gerhart

Bobby Race1 Race2 Race3 Race4 Race5 Race6 Race7 Race8 Race9 Race10

1 42 20 25 27 14 17 19 16 20

Gibson Mark Race1 Race2 Race3 Race4 Race5 Race6 Race7 Race8

32 34 39 38 27 29 30 31

Goess Craig Race1 Race2 Race3 Race4 Race5 Race6 Race7 Race8 Race9 Race10 Race11

Race1

2

Rac

e1

3

Race1

4

Race1

5

Race1

6

Race1

7

Race

18 Race19

Rac

e2

0

34 13 2 2 4 14 1 6 8 2 3 9 8 11 5 7 2 13 3 5

Graham

Buster Race1 Race2 Race3 Race4 Race5

17 17 13 9 20

Gresham

Max Race1

6

Hackenbracht

Chad Race1 Race2 Race3 Race4 Race5 Race6 Race7 Race8 Race9 Race10 Race11

Race1

2

Rac

e1

3

Race1

4

Race1

5

Race1

6

Race1

7

Race

18 Race19

14 2 21 3 8 7 2 21 8 26 6 6 25 1 10 6 3 31 24

Harmon Mike Race1 Race2

32 39

Henriksen AJ Race1 Race2 Race3

8 18 15

Hessert Tom Race1 Race2 Race3 Race4 Race5 Race6 Race7 Race8 Race9 Race10 Race11

Race1

2

Rac

e1

3

Race1

4

Race1

5

10 9 13 4 5 5 11 24 21 9 29 2 4 6 1


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Hillenburg

Andy Race1

28

Hudson Brett Race1 Race2

36 25

Hylton James Race1 Race2 Race3 Race4 Race5 Race6 Race7 Race8 Race9 Race10 Race11

Race1

2

Rac

e1

3

Race1

4

Race1

5

Race1

6

Race1

7

Race

18 Race19

38 33 25 18 34 26 22 22 25 27 24 22 32 30 24 27 22 24 29

Igdalsky Nick Race1 Race2 Race3 Race4 Race5

34 21 17 19 19

Jarvis Dutch Race1 Race2 Race3 Race4

4 17 24 32

Kaltreider

Brian Race1 Race2

15 18

Keselowski

Brian Race1 Race2 Race3 Race4 Race5 Race6 Race7

5 15 13 14 18 22 24

Kile Mikey Race1 Race2 Race3 Race4 Race5

16 4 12 22 6

Kimmel Frank Race1 Race2 Race3 Race4 Race5 Race6 Race7 Race8 Race9 Race10 Race11

Race1

2

Rac

e1

3

Race1

4

Race1

5

Race1

6

Race1

7

Race

18 Race19

23 17 2 7 2 4 6 7 11 7 5 3 1 4 2 1 9 4 6


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Kimmel

Frankie Race1

7

Kimmel Will Race1 Race2 Race3 Race4 Race5 Race6 Race7 Race8 Race9 Race10 Race12

Race1

3

Rac

e1

4

Race1

5

Race1

6

Race1

7

3 25 27 6 26 34 30 27 5 38 10 34 9 27 11 25

King Clint Race1 Race2 Race3 Race4 Race5 Race6

5 6 4 12 6 5

Koch Mike Race1 Race2 Race3 Race4 Race5

28 22 31 31 19

LaJoie Corey Race1 Race2 Race3 Race4 Race5

1 1 4 1 25

LeMastus Bo Race1 Race2 Race3 Race4 Race5 Race6

16 21 27 31 32 19

Lofton Justin

Lofton Matt Race1 Race2 Race3

9 20 5

Marks Jared Race1 Race2 Race3 Race4 Race5 Race6 Race7 Race8 Race9 Race10 Race11

Race1

2

8 16 10 10 7 16 9 25 13 29 12 11


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Marks Justin Race1 Race2 Race3 Race4

27 8 21 11

Martel Kyle Race1 Race2

32 10

Mathews

Ryan Race1 Race2 Race3 Race3 Race5

8 18 20 22 15

Mattioli

chase Race1

18

McCumbee

Chad Race1 Race2 Race3 Race4 Race5 Race6 Race7 Race8 Race9 Race10 Race11

Race1

2

Rac

e1

3

Race1

4

Race1

5

Race1

6

Race1

7

Race

18 Race19

8 20 9 7 3 4 6 8 7 15 28 7 26 1 10 7 9 8 3

McReynolds

Brandon Race1 Race2

11 1

Merrell Matt Race1

12

Mingus

Mason Race1 Race2 Race3 Race4 Race5 Race6 Race7 Race8 Race9 Race10 Race11

Race1

2

Race1

3

Race1

4

Race1

5

Race1

6

Race1

7

Race

18 Race19

Race2

0

Race2

1

7 4 10 2 2 9 6 6 10 12 6 8 6 2 16 5 12 7 9 10 9

Mitchell

Mason Race1 Race2 Race3 Race4

10 5 5 7


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O Leary IV,

Tommy Race1 Race2 Race3 Race4 Race5 Race6 Race7 Race8 Race9 Race10 Race11

Race1

2

Rac

e1

3

Race1

4

Race1

5

Race1

6

Race1

7

32 34 34 21 23 23 24 21 34 25 30 27 25 13 24 26 31

Poole

Brenman Race1 Race2 Race3 Race4 Race5

1 3 1 9 4

PraytorThomas Race1 Race2 Race3 Race4 Race5 Race6 Race7 Race8 Race9 Race10 Race11 Race12

Rac

e13 Race14 Racce15 Race16 Race17 Race18 Race19

Rac

e20 Race21

22 16 21 22 18 10 16 10 16 9 23 17 24 18 21 14 20 21 19 19 19

Rabenold

Kory Race1 Race2 Race3

16 15 16

Ranger

Andrew Race1

17

Richards Josh Race1 Race2 Race3

4 9 15

Roderick

Casey Race1 Race2 Race3 Race4

19 26 18 7

Ruston

Kenzie Race1 Race2 Race3 Race4

8 6 4 9

Schacht Rob Race1 Race2 Race3 Race4 Race5 Race6


14/26


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15

17 13 15 16 14 8 5 2

Steele Tim Race1 Race2 Race3 Race4 Race5 Race6

8 6 5 4 12 9

Thompson

Mark Race1 Race2 Race3 Race4

7 9 15 4

Townley,John Wes Race1 Race2 Race3 Race4 Race5 Race6 Race7 Race8 Race9 Race10 Race11

Race12

Rac

e13

Race14

Race15

Race16

Race17

Race18 Race19

14 8 7 5 3 17 20 22 24 13 6 2 2 6 1 18 23 16 11

Williams Josh Race1 Race2 Race3 Race4 Race5 Race6 Race7 Race8 Race9 Race10 Race11

Race1

2

Rac

e1

3

Race1

4

Race1

5

Race1

6

Race1

7

Race

18

6 3 2 9 8 5 10 15 13 11 18 24 27 21 14 3 2 9

Youster Levi Race1 Race2 Race3 Race4 Race5

6 3 2 8 15


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Names of RacerNumber of Race

Total Income ($) Income per Race ($) Racers' Average Rank

Allgaier, Justin 30 races 813.290 27109 8,42

Armstrong Caleb 19 races 250.000 13157 30,2Armstrong Dakoda 22 races 200.000 6060 9,16

Arpin steve 33 races 252.563 7653 21

Baiard Bill 20 races 142.177 7108 14.3

Basham Darrell 31 races 415.658 13408 31,5

Benjamin Kyle 14 races 189.345 13524 23,1

Berte Tom 19 races 133.500 7026 21,2

Blackburn Steve 19 races 202.145 10639 4,5

Blaney Ryan 33 races 436.117 13215 3,3

Blankenship John 5 races 20000 4000 10,5

Boat Chad15

races 213.000 142007Boston Justin 21 races 477.000 22714 9,8

Bourque Pierre 19 races 24.586 1294 15

Bowen Anderson 19 races 62.500 2976 12,6

Bowman Alex 19 races 745000 39210 8,5

Brent Robb 19 races 20908 1100 9,5

Brevak Brent 19 races 313.687 16509 28,3

Buescher Chris 21 races 178.369 8493 17,7

Buescher James 19 races 105.280 5541 17,3

Bujdoso Robert 16 races 523.789 32736 11,6

Canache Nelson 21 races 187.897 187,897 8951 18,1

Carter Roger 21 races 650.000 30952 32,7

Charlson Drew 19 races 201.356 10597 20,3

Chastain Benny 21 races 16500 785 28,8

Corr Sean 12 races 186.674 15556 25,8

Coulter Joey 19 races 96450 5081 21

Cox Ron 19 races 23910 1258 17

Cross Brent 19 races 12165 640 22,5

Cushman George 19 races 154.143 8112 14,7

Dillon Ty 33 races 257.763 7811 4,3

Dufault Maryeve 30 races 49.128 1637 22,6

Duno Milka 19 races 137.125 7217 22,308

Elliot Chase 20 races 145.134 7256 22,5

Enfinger Grant 22 races 147.454 6702 9,3

Evans Jr. Charles 13 races 150.457 11573 18,2

Ferns Taylor 21 races 155.565 7407 12,5

Fike AJ 19 races 168.434 8864 24

Finley Chad 20 races 253.133 12656 12,6

Fowler Kyle 18 races 442.578 24587 25,2

Fox Steve 19 races 335.987 17683 22,3

Gale Cale 19 races 143.566 7556 24

Gallagher Spencer 21 races 567.454 27021 7


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18

George, Jr. Tim 19 races 342.122 18006 11,5

Gerhart Bobby 19 races 54.520 2869 11,473

Gibson Mark 20 races 154.110 7705 20,1

Goess Craig 12 races 454.243 37853 32,5

Graham Buster 19 races 185.233 9750 7,6

Gresham Max 19 races 398.756 20987 15,2

HackenbrachtChad 19 races 657.898 34626 6

Harmon Mike 19 races 756.143 39797 11,789

Henriksen AJ 19 races 343.235 18065 35,5

Hessert Tom 15 races 656,778 43785 13,667

Hillenburg Andy 23 races 245,687 10682 10,2

Hudson Brett 19 races 189.598 9978 28

Hylton James 19 races 210.334 11070 30,5

Igdalsky Nick 21 races 405.105 19290 28

Jarvis Dutch 9 races 200.347 22260 26,5

Johnson Jerick 14 races 225.337 16095 22Jones Erik 4 races 195.154 48788 19,25

Jones Rob 24 races 354.443 14768 16,5

Jones Terry 3 races 102.265 34088 15,856

Jones Ted 19 races 462.375 24335 12

Keselowski Brian 19 races 419.338 22070 6,367

Kimmel Abby 5 races 177.573 35514 7

Kimmel Frank 19 races 452.185 23799 21,1

Kimmel Frankie 19 races 357.377 18809 6,3

Kimmel Will 17 races 298.457 17556 26,2

King Clint 6 races 657.365 109560 6,4Koch Mike 5 races 528.125 105625 24,3

LaJoie Corey 5 races 285.654 57130 11,3

LeMastus Bo 5 races 254.323 50864 13,8

Lofton Justin 21 races 370.576 17646 16,75

Lofton Matt 19 races 287.569 15135 21

Marks Jared 12 races 365.245 30437 16,6

Marks Justin 20 races 200.869 10043 18

Martel Kyle 19 races 224.760 11829 9,7

Mathews Ryan 23 races 354.772 15424 6

Mattioli chase 19 races 163.873 8624 12McCumbee Chad 19 races 240.774 12672 7,523

McReynolds

Brandon 19races 193.664 10192

6,75

Merrell Matt 19 races 485.987 25578 26,3

Mingus Mason 12 races 277.183 23098 3,6

Mitchell Mason 4 races 364.547 91136 17,857

O Leary IV, Tommy 17 races 154.447 9085 17

Poole Brenman 15 races 260.798 17386 9,3

Praytor Thomas 6 races 175.652 29275 17,5

Rabenold Kory 14 races 382.557 27325 6,75

Ranger Andrew 1 races 37235 37235 11,8


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Richards Josh 3 races 174.582 58194 15

Roderick Casey 4 races 207.228 51807 6

Ruston Kenzie 4 races 165.347 41336 10,75

Schacht Rob 6 races 160.988 26831 9,857

Schenkel Kent 19 races 163.776 8619 10,1

Schrader Ken 21 races 749.047 35668 6,5

Shearer Dale 4 races 183.340 45835 10

Sheltra Patrick 1 races 10986 10986 11,25

Silas Bryan 7 races 593.999 84825 7,3

Simko Michael 10 races 188.779 18877 8,75

Smith Brad 2 races 60545 30272 11,473

Smith Jesse 2 races 10600 5300 11,1

Speer Tyler 19 races 243.552 12818 6,8

Steele Tim 23 races 293.415 12757 15,7

Thompson Mar 3 races 23675 7891 13,2

Townley, John Wes 19 races 147.685 7771 15Williams Josh 18 races 128.773 7154 22,35

Youster Levi 5 races 293.662 58732 24,7

9.166666667 8 8 1 20

The table shows annual income of each driver and average income per race of each driver. The data

was collected from internet. The website source is dir.yahoo.com/recreation/sports/auto

racing/teams/

Calculation

Mean

General formula to calculate mean is shown below:

With:

x = mean

fi= total amount of the data

xi = value of the data


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20

Mean that I calculated here is first, the average rank of each racer, second, the average income a

racer received per race, third, mean of racers salary, and forth, mean of racers rank.

Following is example of calculation of the average rank of each racer; the data is from ArmstrongCaleb ranks:

Following is example of calculation of the average income a racer received per race, the data is from

Armstrong Caleb income:

Following is calculation of mean of racers salary:

258549.5Following is calculation of mean of racers rank:

15.70636277


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Lower quartile

To find out lower quartile, I looked at the drivers race data to find out the drivers lowest rank.

According to the first driver, the drivers lower quartile was 37 which the lowest rank was 37 during

the race. It also relates to the income of the drivers. By looking at the drivers income, I could find

out that which driver had lowest income by looking at each drivers income per race. According tothe drivers income, I could see that the lower quartile was $640 per race. It does not mean that he

does not have any experience, but the driver did not join enough race. The amount of income

impacts on the number of race that the driver has taken.

Calculation:

Race1 Race2 Race3 Race4 Race5 Race6 Race7 Race8

2 11 23 7 8 1 5 1

The result came out with 1 because the lowest rank was 23 from the total of 8 races.

Upper quartile

I gathered data of upper quartile to find out the drivers highest rank and which driver has earned

highest income during the race. By looking at the data of the first driver, I found out that the drivers

upper quartile was 1 which the highest rank was rank 1 during the race. I also related to upper

quartile on drivers income. I found out that which driver had highest income which I can lead as

upper quartile. I found out that the upper quartile of income is $91136 per race. It shows that thedriver earned high income annually and joined many races during period of time. It indicates that

the driver had enough experience on driving and joined many races.

Calculation:

Race1 Race2 Race3 Race4

17 26 24 18

According to the result, the result of upper quartile is 17 which was the best result from 4 races. It

shows that the highest rank was 17.

I calculate mean and quartile using formula in Ms. Excel. The steps I used is as follows. First, I typed

the raw data in Ms. Excel. Second, I type the necessary formula to find the result of mean and

quartile. The formula basically calculates mean and quartile in the same way as examples of my

calculation above.

Hypothesis Testing


22/26

22

My hypothesis is that there is a correlation between racers income and their performance.

Performance will be based on their average rank in the races they had competed in.

To test this hypothesis I will firstly, show the graph that plot the income per race of each driver

against their performance. Secondly, I will calculate the r2using 2 variable statistical analysis. Lastly, I

will check how strong the correlation between those two variables using chi squared test.

According to this graph, there is a best line of fit which shows relationship between the drivers rank

and their income. The best line of fit shows from 1 to 35 which is below 290,000. The method isshown as y=-1650.5x+284630. The graph shows that the strength of the relationship is not accurate

which the data is spreaded around.

Y=-1650.5 x35 +284630

= 226876

The actual estimated value shows 290000, on the other hand it is not exactly the same. It shows the

percentage error between them.

Error=estimated error- actual value

Error= 226876-290000

Error= -63124

In this case, it shows that there is a percentage error.

Percentage error=

y = -1660.5x + 284630

0

100,000

200,000

300,000

400,000

500,000

600,000

700,000

800,000

900,000

0 10 20 30 40

Series1Linear (Series1)


23/26

23

Percentage error= 21.7%

The above graph showed the Racers' Average Rank versus Racers' Income per Race. The graph is

presented using Scatter-Plot Graph. The objective of this graph is to know the correlation between

the two separate variables. The first variable is called the independent variable; it is the Racers

average rank. Its presented in the x line. The value of x is calculated previously by dividing the ranks

of each driver with the total number of race that particular driver participated in. the secondvariable is called the dependent variable, its the Racers income per race. The value is presented in

the y line and its been calculated before. The racers income per year isthe result from the racer

total income with the total number of race that particular racer has participated in.

The graph presented is the first step to figure out the correlation between the independent and the

dependent variable. The purpose of the line in the graph is to connect the dots in the graph. The line

will show the possible correlation between variable x and variable y. If the Racers average rank

correlate with the Racers income per race it will be proven in the test that will be done below.

According to the table, it shows that the x value and y value is not correlated which the data is

spread around. It does not really connect one to another value in this graph according to the racersrank and their income. On the other hand, it leads between racers income per race, annual income

and their average rank which can be relate to each other.

First of all, we have to the 2 variable statistics analysis.

21028.89333

92195241140

0

20000

40000

60000

80000

100000

120000

0 5 10 15 20 25 30 35 40

Racers'incomeperrace

Racers' average rank

Racers' Average Rank versus

Racers' Income per Race


24/26

24

1680.58081633676709.78n = 109

The value of r2 calculated is shown above. The value is quite small. Usually it indicates a small

correlation between x variable and y variable. The accuracy of the calculation is determined by how

many rounding we done throughout the calculation. In this calculation I did not do any rounding so

the accuracy is quite high. The next step to figure out how strong correlation between two variables

is to determine the r2 critical using chi squared test.

If the r2 calculated > r2critical; then the correlation is high. Otherwise, its weak, if its too weak then

I can say that theres no meaningfulcorrelation between these two variables.

Using 2 var stats analysis:

Below Average

Performance

Above Average

Performance

Total

Below Average Income 35 45 80

Above Average Income 19 10 29

Total 54 55 109

fo fe fo-fe (fo-fe)2 (fo-fe)2/fe

24 12.6 11.4 129.96 10.31429

14 6.8 7.2 51.84 7.623529


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25

4 10.5 -6.5 42.25 4.02381

3 8.6 -5.6 31.36 3.646512

Hypothesis:

H0(null hypothesis)= the income is independent of the racers rankH1 (alternate hypothesis) = the income is dependent of the racers rank

To find the degree of freedom (df), we use the equation v = (r-1) (c-1), where r = the number of race

and c = number of columns v = (2-1) (2-1)

According to the calculation the degree of freedom is 1. Testing this at a 10% significance level.

r2critical = 2.67

r2calculated = r

2calculated < r

2critical

Since the r2 calculated < r2 critical, we reject the H1 hypothesis and accept the null hypothesis. It

means there is no strong correlation between the Racers average rank and the Racers income per

race.

Conclusion:

After doing this investigation, I learned that it was very challenging and interesting to

research about my project. I found out that there was a relationship between the drivers

performance and their income. I found out that, according to the drivers rank from the race, it can

relate into their income. According to this, it indicates that the driver who joined more races, the

driver earned more income because each driver earned more income every time when the driver

joined races. However, every driver had different income of annual. It shows that the driver who had

longer experience of driving and joined more races, they seem to have higher wages. According to

the result, I found out that the performance of drivers were quite reasonable. Most of driver had

quite high performance according to their rank and number of race that they have joined. Some of

drivers improved their driving skills by joining more races. To gather the data, I recorded my data

from the website such as gathering data of drivers name, rank, number of races, and their income.

As a result of control variables, the result was constant and there was no great difference between

each drivers performance. On the other hand, there was great difference between drivers income

because every driver did not join every races. By doing this investigation, I caused some problems on

figuring about what kind of mathematics that I am going to use and calculations. To improve this, I

must make sure about my topic and question what I am going to investigate and spend more time

on figuring out mathematical problems. Next time, if I had to do this investigation again, I could

come out with another outcome to figure out more mathematical problems on this investigation

which I can show more problems and relationship between one to another outcome by gatheringmore data.


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Documents

First Draft of Math IA