Maths Coursework - Used Cars
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Introduction
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”
Middle
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
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.
This student written piece of work is one of many that can be found in our GCSE Gary's (and other) Car Sales section.
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