Maths Coursework – Used Cars

There are many factors that can influence the price of a second hand car, such as; model, make, age, engine size, mileage etc. For this coursework I will be using the following three factors in order for me to investigate what effects the price of a second hand car:

• Age
• Mileage
• Engine size

My reasons for choosing these three factors are as following:

Age:

People are more likely to acquire a car, which is new than old because old cars are commonly not as popular as the new ones as they are more likely to break down. Also, the public (especially the younger generation), would prefer to buy a new car because they are much more fashionable to have.

Mileage:

The mileage will be an important factor affecting the price of a second hand car because a car with a high mileage means that it has been driven a lot and this means that it is more likely to break down. Also it means that high maintenance will be required for the car to stay working whereas a car with a low mileage wouldn’t entail as much maintenance.  

Engine Size:

The engine size is also another factor, which will affect the price of the second hand car greatly. The reason is that the larger the engine means that the quicker the car will go and in today’s society, a fast car would be essential and appeal to a lot of people.  

For this investigation, I have come up with the following hypothesis:

“The mileage affects the price of a second hand car more than the engine size and the age of the car”

Fiat

Bravo

10810

4995

1.4

18500

2

53.79278446

Fiat

Punto

7518

3769

1.1

38000

4

49.8669859

Fiat

Punto

8601

3995

1.2

31000

4

53.55191257

Fiat

Cinquecento

6009

1995

0.9

20000

6

66.7998003

Ford

Orion

16000

7999

1.8

7000

1

50.00625

Ford

Escort

8785

1595

1.3

68000

7

81.84405236

Ford

Fiesta

7875

1495

1.8

74000

11

81.01587302

Ford

Fiesta LX

8748

1995

1.1

60000

7

77.19478738

Ford

Escort

12125

4295

1.4

29000

3

64.57731959

Ford

Escort

11800

4700

1.8

34000

5

60.16949153

Ford

Fiesta

8680

3200

1.8

27000

4

63.13364055

Ford

Puma

13230

8250

1.4

34000

3

37.64172336

Ford

Escort

13183

3495

1.8

43000

7

73.48858378

Ford

Mondeo

17780

7995

2

30000

4

55.03374578

Ford

Fiesta

6590

1664

1

37000

10

74.74962064

Ford

Fiesta

7310

1050

1.1

90000

8

85.63611491

Ford

Escort

9995

2995

1.3

64000

6

70.03501751

Rover

623 Gsi

22980

6999

2.3

30000

4

69.54308094

Rover

416i

13586

3795

1.6

49000

6

72.06683351

Rover

114 Sli

8595

2495

1.4

33000

6

70.97149506

Rover

Metro

6645

895

1.1

43000

7

86.53122649

Rover

214i

9565

1700

1.4

55000

8

82.22686879

Rover

623GSi

24086

2975

2.3

96000

5

87.64842647

Rover

Club

19530

14999

1.8

2000

1

23.20020481

Rover

623 GSi

24086

2975

2.3

96000

6

87.64842647

Rover

Metro

5495

1995

1.1

52000

7

63.69426752

Rover

416i

14486

3685

1.6

64000

6

74.56164573

Vauxhall

Vectra

18580

7999

2.5

20000

2

56.94833154

Vauxhall

Tigra

13510

7499

1.4

27000

4

44.49296817

Vauxhall

Vectra

18140

6499

2.5

49000

4

64.17309813

Vauxhall

Corsa

8900

4995

1.6

24000

2

43.87640449

Vauxhall

Nova

5599

1000

1.4

75000

10

82.1396678

Vauxhall

Corsa

7840

4976

1.4

21000

4

36.53061224

Vauxhall

Corsa

7440

3495

1.2

55000

6

53.02419355

Vauxhall

Astra

9795

3191

1.4

43000

6

67.42215416

Vauxhall

Vectra

13435

4995

1.8

52000

5

62.82098995

I have found the percentage depreciation for each car. I will now draw scatter graphs for age, engine size and mileage plotted against the percentage depreciation, for each car.

Comparing the graphs for age

I have drawn the scatter diagrams and they each have a trend line passing through them, which is called the linear trend line. Its function is to estimate the percentage depreciation rate for the second hand price car, taking into account all the input values, and then work out a gradient, which tells us a lot about the relationship between the two variables the graph is based upon.

All the graphs have positive correlation, some strong (Fiat and Rover), and some weak (Vauxhall and Ford). All the graphs show some sort of positive correlation, which means that as the age increases, the percentage depreciation increases and thus the second hand price decreases. Rover has the steepest gradient, which suggests that age has a higher value for Rover than any other car make. Ford has the gentlest gradient, which suggests that the age has a lower value on Ford than any other car make.

The second trend line I used is the curvy one, which is called the polynomial trend line. It is used to show how fast the second hand price for each car decreases. If you look carefully at the trend line, you will notice that when the car is young i.e.

Conclusion:

In my investigation I have found that the age affects the second hand price the most since the correlation was strong and there were fewer outliers in the scatter graphs. This is followed by mileage as identical correlations were found and fewer outliers. The least most influential factor to the second hand price of the cars will be the engine size, as it had the most outliers and the graph correlations were not the same for each car make. This means that my hypothesis was incorrect because the mileage follows the age.    

If I had additional time I would have used standard deviation which measure the spread and results are more reliable. I also would have proved using coefficient of covariance that age is the factor that affects the second hand price the most. Coefficient of covariance or r gives a value which can terminate which factor is most important. If r = +1, this indicates the correlation is positive. If the value of r is close to +1 then that means the correlation is stronger that the value that is away from +1. The same thing is with -1 which indicates that the correlation is negative. So the closer the value of r is to -1, the stronger the negative correlation. I would’ve used this method to find the values of r for mileage, age and engine size for all four makes. This would have proved which factor influences the second hand price of a car the most.

If I had used more data for this investigation, then the results would have been more concise and reliable. Also, the gradients of the scatter graphs would have been clearer and so would the box plots.