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  • Level: GCSE
  • Subject: Maths
  • Word count: 4114

used car coursework

Extracts from this document...

Introduction

Sukhraj Dhillon

11x1

Used car coursework

This coursework is about what influences the price of a second hand car. In this coursework I will be comparing the second hand prices of cars, using different factors. There will be tables and graphs showing the four most popular cars. I will be writing about how mileage, age, used car price and engine size of different cars affect their second hand prices. This will help me show which car has the biggest depreciation rate.    

My hypotheses are:

  1. As the mileage increases the second hand price will decrease.
  2. The bigger the engine size the higher the price of the second hand car.
  3. The older the car the cheaper it will be.
  4. The higher the price of the car when brought the less it depreciates.

I will be using scatter diagrams to show the correlation. I will also use box and whiskers to show the median and compare the ranges of second hand price. I expect all four hypotheses to be correct because logically if the mileage increases the price of the car should automatically decrease. It is the same for the rest of the hypotheses.

Stratified sampling

I choose the four most popular cars in order to conduct the stratified sampling.

Make

Quantity

Ford

16

Vauxhall

13

Rover

12

Fiat

10

Total

51

The method of sampling I will use is fair and easy to do. My chosen sample size is 35. The formula I will b using is:

Car make = Total no. of car make       x Sample size

                       Total no. of cars

Ford = 16   x  35 = 11

            51

Vauxhall =  13   x  35 =  8

                    51

Rover =  12   x  35 = 8

               51

Fiat =  10   x  35 =7

            51

I used stratified sampling because every group is represented in an identical quantity. So I can get a good representation of the complete population. The main reason why I used sampling was as it reduces the time taken to process.

Scatter diagram work

Mileage

Age

Used car price

Engine size

1

7000

1

7999

1.8

2

68000

7

1595

1.3

3

60000

7

1995

1.1

4

64000

7

2300

1.4

5

29000

3

4295

1.4

6

34000

5

4700

1.8

7

27000

4

3200

1.8

8

43000

7

3495

1.8

9

37000

10

1664

1

10

57000

5

3995

1.8

11

64000

6

2995

1.3

This table shows the 11 Ford cars out of 16 which were selected through stratified sampling. The table shows the cars mileage, age, used car price and engine size.

image00.png

This scatter diagram shows the affect on the used car price as the age increases. I added a trend line and it goes in a down ward slope from left to right. This indicates to us that the graph is showing us a negative correlation between the used car price and the age. From the graph I can say that the older the car is the lower the value is of the car. The equation of the line is:

y = - 649.6x + 7137.1

The gradient is -649.6 and this tells us that every time the age of the car increases by 1 year the value of the car decreases by £649.60. The intercept of the line is 7137.1 and this tells us that if the car had an age of 0 years then the price would be £7137.1.

image01.png

This scatter diagram shows the affect on used car price as the mileage increases. The trend line I added shows a slope going downwards from left to right. It shows a negative correlation between used car price and mileage. From the graph I can say that as the mileage increases the used car price decreases. The equation of the line is:

y = - 0.07704 + 6612.5

The gradient is -0.07704 and this tells us that every time the mileage increases by 1 mile the used car price will decrease by £0.07. The intercept of the line is 6612.5 and this tells us that if the mileage is 0 then the used car price will be £6612.5.

image12.png

This scatter diagram shows the affect on used car price as the engine size increases. The trend line I added shows a slope going upwards from left to right. It shows a positive correlation between used car price and engine size. From the graph I can say that as the engine size increases the used car price increases. The equation of the line is:

y = 3967.9x – 2476.1

The gradient is 3967.9 and this tells us that every time the engine size increases by 1 the used car price will increase by £3967.90. The intercept of the line is -2476.1 and this tells us that if the mileage is 0 then the used car price will be -£2476.1.

Used car price

New car price

7999

16000

1595

8785

1995

8748

2300

9105

4295

12125

4700

11800

3200

8680

3495

13183

1664

6590

3995

15405

2995

9995

This table compares the used car price to the new car price of Ford cars.

image18.png

This scatter diagram compares the new car price against the used car price of Ford cars. The trend line I added shows a slope going upwards from left to right. It shows a positive correlation between new car price and used car price. From the graph I can say that as the used car price increases the new car price increases. The equation of the line is:

y = 1.3597x + 6221

The gradient is 1.3597 and this tells us that every time the used car price increases by £1 the new car price will increase by £1.36. The intercept of the line is 6221 and this tells us that if the used car price is £0 then the new car price will be £6221.

Mileage

Age

Used car price

Engine size

1

20000

2

7999

2.5

2

75000

10

1000

1.4

3

73000

10

850

1.6

4

58000

6

2990

1.6

5

21000

4

4976

1.4

6

55000

6

3495

1.2

7

63000

6

6995

2

8

43000

6

3191

1.4

9

52000

5

4995

1.8

...read more.

Middle

y = -0.0815x + 8218.6

The gradient is -0.0815 and this tells us that every time the mileage increases by 1 year the used car price will decrease by £0.0815. The intercept of the line is 8218.6 and this tells us that if the mileage is 0 then the used car price will be £8218.6.

image21.png

This scatter diagram shows the affect on used car price as the engine size increases. The trend line I added shows a slope going upwards from left to right. It shows a positive correlation between used car price and engine size. From the graph I can say that as the engine size increases the used car price increases. The equation of the line is:

y = 4545.5x - 3470.8

The gradient is 4545.5 and this tells us that every time the engine size increases by 1 the used car price will increase by £4545.50. The intercept of the line is 3470.8 and this tells us that if the engine size is 0 then the used car price will be - £3470.80.

Used car price

New car price

7999

18580

1000

5599

850

10150

2990

13740

4976

7840

3495

7440

6995

18675

3191

9795

4995

13435

This table compares the used car price against the new car price of Vauxhall cars.

image22.png

This scatter diagram compares the new car price against the used car price of Vauxhall cars. The trend line I added shows a slope going upwards from left to right. It shows a positive correlation between new car price and used car price. From the graph I can say that as the used car price increases the new car price increases. The equation of the line is:

y = 1.4914x + 5648.1

The gradient is 1.4914 and this tells us that every time the used car price increases by £1 the new car price will increase by £1.49. The intercept of the line is 5648.1 and this tells us that if the used car price is £0 then the new car price will be £5648.10.

Mileage

Age

Used car price

Engine size

1

51000

6

3795

2

2

49000

6

3795

1.6

3

33000

6

2495

1.4

4

96000

5

2975

2.3

5

66000

5

3400

2

6

2000

1

14999

1.8

7

64000

6

3685

1.6

8

52000

7

1995

1.1

This table shows the 8 out of 12 Rover cars chosen using stratified sampling. The table shows the mileage, age, used car price and the engine size.

image23.png

This scatter diagram shows the affect on used car price as the age increases. The trend line I added shows a slope going downwards from left to right. It shows a negative correlation between used car price and age. From the graph I can say that as the age increases the used car price decreases. The equation of the line is:

y = -2192.4x + 16152

The gradient is -2192.4 and this tells us that every time the age increases by 1 year the used car price will decrease by £2192.40. The intercept of the line is 16152 and this tells us that if the age is 0 then the used car price will be £16152.

image24.png

This scatter diagram shows the affect on used car price as the mileage increases. The trend line I added shows a slope going downwards from left to right. It shows a negative correlation between used car price and mileage. From the graph I can say that as the mileage increases the used car price decreases. The equation of the line is:

y = -0.1119x + 10420

The gradient is -0.1119 and this tells us that every time the mileage increases by 1 year the used car price will decrease by £0.1119. The intercept of the line is 10420 and this tells us that if the mileage is 0 then the used car price will be £10420.

image02.png

This scatter diagram shows the affect on used car price as the engine size increases. The trend line I added shows a slope going upwards gradually from left to right. It shows a positive correlation between used car price and engine size. From the graph I can say that as the engine size increases the used car price increases. The equation of the line is:

y = 1794.5x + 1546.8

The gradient is 1794.5 and this tells us that every time the engine size increases by 1 the used car price will increase by £1794.50. The intercept of the line is 1546.8 and this tells us that if the engine size is 0 then the used car price will be £1546.80.

Used car price

New car price

3795

21586

3795

13586

2495

8595

2975

24086

3400

17795

14999

19530

3685

14486

1995

5495

This table compares the used car price against the new car price of Rover cars.

image03.png

This scatter diagram compares the new car price against the used car price of Rover cars. The trend line I added shows a slope going upwards from left to right. It shows a positive correlation between new car price and used car price. From the graph I can say that as the used car price increases the new car price increases. The equation of the line is:

y = 0.5043x + 13304

The gradient is 0.5043 and this tells us that every time the used car price increases by £1 the new car price will increase by £0.5043. The intercept of the line is 13304 and this tells us that if the used car price is £0 then the new car price will be £13304.

Mileage

Age

Used car price

Engine size

1

31000

4

3995

1.2

2

20000

6

1995

0.9

3

51000

8

1495

1

4

32000

7

1500

1.4

5

13000

3

4500

1.2

6

18500

2

4995

1.4

7

38000

4

3769

1.1

...read more.

Conclusion

image17.png

Conclusion

Overall form looking at my results I have found out that there are many different factors that influence the price of second hand cars. My sample was very useful as it allowed me not to be bias in the cars I choose. Also looking at information from a scatter diagram made it easy to make relationships between the second hand price and factors which affect it. I feel that the sample was not as accurate as I had used more cars for some makes than others. From this I saw that the factor which had the most affect on second hand price was age and engine size of the car. To work this out I looked at the gradient of the line on my scatter diagram and compared them. The age and engine size had the steepest line so they had the greatest affect on second hand price. For most factors the correlation of between the population and sample were weak because the sample was not big enough to represent the population. The tend line can be used to predict the future price of the car as each factor changes. When comparing the makes I learnt that each factor had similar affect on different cars. The cheapest car to buy from the cars in my sample was a Vauxhall Cavalier which was £850. The car which depreciated the most over the years was Rovers as the trend line on the scatter diagram had the steepest gradient. All my hypotheses were right which I stated before I started the project. The weakness of this project is that my sample was not big enough for the population of cars that are in the U.K right now which are millions. So next time if I was to do this project again I would use a bigger sample to make my results and predictions more reliable.


Maths coursework

...read more.

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