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  • Level: GCSE
  • Subject: Maths
  • Word count: 4738

Maths Coursework: Car Prices and Specifications

Extracts from this document...

Introduction

Hee-Who Park        Used Cars Sales         04/02/01

11AM        Maths Coursework                

Maths Coursework:

Aim:

        The aim of my investigation in this maths coursework is to investigate the used car sales. I will need to investigate on these variables:

  • The price of the cars
  • The age of the cars
  • The makes of the cars
  • The cost when new of the cars
  • The mileage of the cars
  • The engine sizes of the cars

All the variables above are ratio variables (Numbers are used) except the makes of the cars, because that one is special and it’s called nominal variables.

I will first try to find out any links between the current price of the car and the other variables such as age, mileage, car engine size, and the make. After finding links, I will then attempt to progress the data in order to find out stronger links between variables and eventually I will try to find a general value or formula that can link them.  I will be drawing some graphs and then look for conclusions, which can help me to find a general formula.

Here is the results table, which was given in this coursework:

Car Number

Price (Pounds)

Age (Years)

Make (Brand)

Original Price (Pounds)

Mileage (Miles)

Engine Size (Litres)

1

6970

3

Ford

11600

24000

1.6

2

3350

7

Peugeot

7100

85000

1.1

3

3995

6

Ford

13800

52000

2

4

5300

6

Vauxhall

16300

70000

2

5

6500

3

Fiat

8700

24000

1.2

6

1500

9

Vauxhall

8700

82000

1.6

7

995

9

Ford

8500

102000

1.8

8

3000

7

Vauxhall

10400

63000

1.7

9

7495

1

Vauxhall

9770

8000

1.4

10

850

10

Ford

7540

124000

1.6

11

5595

4

Ford

11000

41000

1.6

12

4995

3

Ford

9880

34000

1.4

13

5595

4

Ford

14000

55000

1.6

14

4995

4

Rover

11500

40000

1.4

15

2600

7

Rover

12000

82000

1.6

16

1000

10

Peugeot

6200

119000

1.1

17

750

11

Peugeot

5100

96000

1

18

1350

8

Ford

9140

108000

1.6

19

2950

8

Ford

17750

96000

2.9

20

3250

7

Vauxhall

9990

86000

1.6

21

5650

3

Vauxhall

11150

34000

1.6

22

4600

2

Rover

7300

17000

1.1

23

5400

1

Rover

7300

11000

1.1

24

4800

1

Rover

7300

26000

1.1

25

2700

5

Fiat

13000

51000

2

26

11000

1

Peugeot

13800

9000

1.8

27

2800

5

Fiat

6500

43000

1

28

8000

4

Rover

21000

142000

2.3

29

6495

2

Ford

8800

23000

1.3

30

4050

4

Ford

8400

48000

1.3

31

6300

2

Ford

10300

26000

1.3

32

4100

4

Vauxhall

8900

37000

1.3

33

6600

1

Vauxhall

8500

9000

1.3

34

7800

1

Peugeot

10500

13000

1.4

35

8700

3

Vauxhall

16000

42000

2

36

2000

7

Peugeot

8300

65000

1.4

Hypothesis:

I predict that all of the variables will affect the Price of the cars in anyway, because they all are very important. So I think the Age will affect the price most, because it is the most important variable of all and I think the Engine Size affects the least, however all the variables will affect it in some ways.

Graphs:

1.

...read more.

Middle

image34.png

This graph clearly shows us that there is no correlation here in this graph between the Engine Size and the Price. The trend shows us that the bigger the engine size, the higher the price. But the relationship is very weak. Although there are 2 cars with the same engine size, the price difference is very big.

From this graph, we can conclude that:

  • The Engine Sizes has no links between the Prices of the cars.

5. Previously, I did a graph on the relationship between the price and the engine size and the correlation came out not very strong. So this time I am going to bring in the Original price instead with the Engine size to see whether these two variables will have some sort of relationships. image42.png

I was surprised to get this kind of result from these two variables. Previously we had tried the graph with the Price and the Engine Size and it did not come out very well because there was no correlation, but this graph shows a strong correlation. This means both of the variables are closely linked. The y-intercept for this graph should show a positive value, because the car without the engine must cost something, but the value comes out as negative, which means there’s an error. From this, the conclusion can be made which are

  • The original price of a car is directly proportional to its engine size.
  • For every increase of one litre of the car’s engine size, its price increases 7528 pounds in average.

6. I think there will be a quite a strong link between the Original Price and the Price (Current price), because the higher the original price is, the higher the car price would be if the other variables don’t play a part in this.

...read more.

Conclusion

The brand Fiat is the cheapest from the rest of the brandsFiat car is quite cheap due to a lot of variation in the size of the engineRover and Vauxhall are technically more expensive than the other brandsFord have the most expensive cars when it is newFord tends to have the biggest engine size than the rest of the brandsAll Peugeot cars have the smallest engine size than the rest of the brands, and that is why it makes them the cheapest cars when it is newThe brands have quite a big impact on the model formulae, and therefore each model formula has to be made for each brands to make the predicted price as near as possible to the real present priceThe average formula for all the brands is: image19.png. This is true, since the gradient and the y-intercept were taken from the graph where the rate of depreciation was against the age. On this particular graph, it was not done with each brand and contained all the brands.
  • The model formulae that is used to each of the brands are as follows:

Fiat: image28.png

Ford: image29.png

Peugeot: image30.png

Rover: image31.png

Vauxhall: image32.png

  • Each specifically specified model for each brands are much more accurate than the model which is the average formula for all the brands. The average formula for all the brands has the error of around ±1000, where as the each brand’s formulae has ±500 pounds of error. So I could conclude that each brands’ model is much more accurate.
  • So it is the best to use the model function formula for each brand to get the most accurate results. But the predicted price may come out slightly faulty, but it would still be much more accurate than using the universal formula for all of the brands.  

                -  -

...read more.

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