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  • Level: GCSE
  • Subject: Maths
  • Word count: 2406

Theory of Whether The Age of a Car Is Directly Proportional To It's Depreciation

Extracts from this document...

Introduction

Hypothesis 1
Age of Car

I shall now be trying to prove whether the age of the car is directly proportional to the depreciation. To test this theory I shall be using a cluster sample. I decided to use the Ford Cars sample because it has a range of cars from the age of 1 – 8 and this may help to get the information more accurate. I shall also be using a sample of Fiat cars to see if my answer is conclusive.

Ford Cars

Age (Years)

Price when new

Price Now

Price lost

% Loss

1

£16,000

£7,999

£8,001

50%

2

£14,505

£8,800

£5,705

39%

3

£13,230

£8,250

£4,980

38%

4

£17,780

£7,995

£9,785

55%

5

£15,405

£3,995

£11,410

74%

6

£9,995

£2,995

£7,000

70%

7

£13,183

£3,495

£9,688

73%

8

£7,310

£1,050

£6,260

86%

Fiat Cars

Age (Years)

Price when new

Price Now

Price lost

% Loss

1

£10,954

£6,795

£4,159

38%

2

£10,810

£4,995

£5,815

54%

3

£7,864

£4,500

£3,364

43%

4

£8,601

£3,995

£4,606

54%

5

£10,351

£3,495

£6,856

66%

6

£10,423

£1,295

£9,128

88%

7

£8,272

£1,500

£6,772

82%

8

£6,864

£1,495

£5,369

78%

To find out the percentage loss of a car I used the formula below:

image00.png

image01.png

I then transferred the data from the tables and then added it to the scatter diagrams.

image17.png

This scatter diagram displays the information on the Ford Cars table.
This scatter diagram displays the information on the Fiat Cars table.
image18.png

Both scatter diagrams above show a positive correlation and this means that as the age of a car increases the cars depreciation or decline in price increases. However, some of the cars do not

...read more.

Middle

53%

58000

£13,740

£2,900

£10,840

79%

63000

£18,675

£6,995

£11,680

63%

73000

£10,150

£850

£9,300

92%

75000

£5,599

£1,000

£4,599

82%

image20.png

The table and graph also follow the same pattern as the Rover Cars and this is confirmation that as the mileage of a car increases the depreciation of the car increases as well.

Hypothesis 3

Engine size and Price

A factor I thought would make a difference to the price of the car is the engine size. The basis for this statement is because I believe that the bigger the engine the more powerful and faster the car is and this means the price of the car would be higher.

For this part of the analysis I shall be using convenience sampling. And I decided to use the first 75 cars. This is so that the answer I get in the end is more accurate and fair.

The stem and Leaf diagram below displays the data I took.

Stem           Leaf

0        9  9  9  5        image08.png

1        0  0  1  1  1  1  1  2  2  2  2  2  3  3  4  4  4  4  4  4  4  4  4  4  4  4  4  4  4  4  5  6 6  6  6  6  6  6  6  6  6  6  8  8  8  8  8  8  8  8  8  8                

2        0  0  0  0  0  0  0  0  0  0  3  3  3  5  5  5  5image11.png

3        0image12.png

4        0

The stem and leaf diagram shows that the mode for the most popular choice of engine size is the 1.4 litre engine and the range of all the cars is from a 0.9 litre engine to a 4-litre engine.

To find out whether the engine size is an important factor on the price I took the 75 cars and put it in the table below. If I had more than one type of the same engine size I found the average price of all the cars.

This tally chart below shows the data for the engine size and price.

Engine size

Tally

Frequency of cars

Average price (£)

0.9

2

£4,547.00

0.95

1

£1,495.00

1

2

£5,247.00

1.1

5

£1,832.00

1.2

6

£3,525.00

1.3

2

£2,695.00

1.4

16

£4,519.94

1.5

1

£1,295.00

1.6

11

£4,601.18

1.8

10

£6,072.40

2

10

£5,069.50

2.3

3

£5,580.00

2.5

4

£3,395.00

3

1

£19,495.00

4

1

£6,250.00

Using the tally chart I created a scatter diagram to show the relationship between engine size and price.

image21.png

image13.png

As you can see from this graph it has a positive correlation. This just shows that as the engine size increases the price also increases. Some of the points on the scatter diagram do not follow the same pattern. For example the arrow that is shown on the graph marks a car with a three-litre engine. This car is worth more than a car with a four-litre engine. This could of happened because something else has affected the price of the car such as the age or the make of the car. Another reason would be because the price of the car is what it is worth now not what its value should be when bought new.

This scatter diagram shows the value of cars when bought new.

image22.png

As you can see it shows a much more accurate result than the other graph but it still shows the same positive correlation but this correlation is much stronger.

This has helped prove my theory that engine size does affect the price of a car.

Hypothesis 4 Make and Model

Now I shall be investigating whether the make of a car has an affect on the price of a car. To find this out I shall be using a quota sample of twelve Ford Cars and twelve Rover Cars. I believe that the Rover Cars will be more expensive because Rover is elegant and more stylish than the Ford so it may be more expensive.

I shall be representing my data using a population pyramid. Below is a table with the data that I took. The price that I have used is the price of the car when it is new.

Rover Cars price (£)

Frequency

Percentage on Pyramid

£0 < p < £5,000

0

0%

£5,000 < p < £10,000

4

33%

£10,000 < p < £15,000

2

17%

£15,000< p < £20,000

2

17%

£20,000 < p < £25,000

4

33%

Ford Cars price (£)

Frequency

Percentage on Pyramid

£0 < p < £5,000

0

0%

£5,000 < p < £10,000

5

42%

£10,000 < p < £15,000

5

42%

£15,000< p < £20,000

2

16%

£20,000 < p < £25,000

0

0%

...read more.

Conclusion

lspacing="0" class="c17">

Make

Model

Price when New

Price Now

Value lost

Percentage lost

Nissan

Micra

5340

1595

3745

70%

Nissan

Micra

7995

3999

3996

50%

Nissan

Sunny

7799

2595

5204

67%

Ford

Fiesta

8680

3200

5480

63%

Daewoo

Lanos

11225

5999

5226

47%

Daewoo

Lanos

9525

4395

5130

54%

Fiat

Bravo

10810

4995

5815

54%

Ford

Escort

11800

4700

7100

60%

Vauxhall

Corsa

8900

4995

3905

44%

Daewoo

Nubira

13850

6895

6955

50%

Fiat

Bravo

10954

6795

4159

38%

Ford

Mondeo

17780

7995

9785

55%

Peugeot

406

17490

7500

9990

57%

Toyota

Corrolla

13800

7495

6305

46%

Volkswagen

Polo

9960

7550

2410

24%

Mercedes

A140 Classic

14425

10999

3426

24%

Mercedes

AvantGarde

17915

11750

6165

34%

Volkswagen

Beetle

14950

13500

1450

9%

Two owners

Make

Model

Price when New

Price Now

Value lost

Percentage lost

Fiat

Uno

6864

1495

5369

78%

Ford

Fiesta LX

8748

1995

6753

77%

Nissan

Micra

6295

1795

4500

71%

Rover

Metro

5495

1995

3500

64%

Fiat

Punto

7518

3769

3749

50%

Ford

Escort

15405

3995

11410

74%

Peugeot

306

12350

3995

8355

68%

Rover

620Si

17795

3400

14395

81%

Vauxhall

Corsa

7440

3495

3945

53%

Vauxhall

Vectra

13435

4995

8440

63%

BMW

316i

13650

6995

6655

49%

Renault

Megane

13175

6999

6176

47%

Vauxhall

Astra

14325

6595

7730

54%

Vauxhall

Vectra

18140

6499

11641

64%

Vauxhall

Calibra

18675

6995

11680

63%

Volkswagen

Golf GTi

16139

6995

9144

57%

Three owners

Make

Model

Price when New

Price Now

Value lost

Percentage lost

Hyundai

Sonnata

11598

1195

10403

90%

Fiat

Tipo

8272

1500

6772

82%

Ford

Escort Duet

9105

2300

6805

75%

Mazda

Pegasus

10420

2495

7925

76%

Rover

820 SLi

21586

3795

17791

82%

Four owners

Make

Model

Price when New

Price Now

Value lost

Percentage lost

Vauxhall

Nova

5599

1000

4599

82%

As there are more owners the percentage lost by the cars increase. Cars with one previous owner lost about an average of 35%. Cars previously owned by two people lost about 65% - 70%, cars that had three owners lost an average of 75% - 80% and cars with four previous owners lost 80+%.

This has helped me to come to the conclusion that number of owners does have an affect on the price. The more previous owners a car has the less it would cost.

...read more.

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