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• Level: GCSE
• Subject: Maths
• Word count: 5661

# In this project we have been given a large amount of data on used cars to work with, and our aim is to analyse this and investigate any possible correlations between cost and other factors given.

Extracts from this document...

Introduction

Maths Coursework – Used Car Data Investigation

Plan

In this project we have been given a large amount of data on used cars to work with, and our aim is to analyse this and investigate any possible correlations between cost and other factors given.

Brainstorm

I have brainstormed all the possible factors affecting the cost of a second hand car below. From these I will select 3 in which to study in detail.

• Mileage
• Age
• Condition
• Fuel
• Make
• Air conditioning
• Insurance group
• Number of owners
• Engine size
• Service
• MPG
• Central locking
• Length of MOT
• Airbags

I will be investigating mileage, age and make of car, primarily because it is easy to gain extra data from other sources on these three, but also because there are possible correlations not only with cost, but also between the three factors I have chosen.

Hypothesis

I have a number of hypothesise which I will explore in this project:

• As mileage increases, the price of the car will decrease
• As age of the car increases, the price of the car will also decrease
• The make of the car will carry higher or lower prices depending on the make; some makes will cause prices to be higher, others will cause prices to be lower.

What I will do in this project

To begin with, I will look at the list I have been given in a general manner, by conducting a brief search through the list, looking at medians, quartiles, etc.

After this I will analyse the above 3 factors and compare them in tables and graphs to the price to find a correlation, in order to come out with a conclusion.

Mileage – from given data

Before studying mileage and it’s effect on price in detail we should briefly examine any possible correlation so we have a better idea of what to look at when studying in depth.

Middle

18

Fiesta

5

7500

3178

4322

57.6

19

Fiesta

7

7500

3088

4412

58.8

20

Fiesta

8

7500

3357

4143

55.2

21

Escort

5

8995

3016

5979

66.5

22

Escort

6

8995

3361

5634

62.6

23

Escort

5

8995

3647

5348

59.5

24

Escort

5

8995

3564

5431

60.4

25

Escort

6

8995

3448

5547

61.7

26

Escort

7

8995

3084

5911

65.7

27

Escort

4

8995

3363

5632

62.6

28

Escort

3

8995

3962

5033

56.0

29

Escort

4

8995

3414

5581

62.0

30

Focus

5

14500

8485

6015

41.5

31

Focus

4

14500

9208

5292

36.5

32

Focus

3

14500

10426

4074

28.1

33

Focus

2

14500

10264

4236

29.2

34

Focus

3

14500

9960

4540

31.3

35

Focus

4

14500

9373

5127

35.4

36

Focus

2

14500

10124

4376

30.2

37

Focus

4

14500

8838

5662

39.0

38

Focus

2

14500

10423

4077

28.1

39

Focus

1

14500

9992

4508

31.1

40

Mondeo

2

16995

8106

8889

52.3

41

Mondeo

5

16995

8706

8289

48.8

42

Mondeo

4

16995

7820

9175

54.0

43

Mondeo

2

16995

9705

7290

42.9

44

Mondeo

4

16995

8746

8249

48.5

45

Mondeo

1

16995

9815

7180

42.2

46

Mondeo

3

16995

9295

7700

45.3

47

Mondeo

3

16995

8590

8405

49.5

48

Mondeo

1

16995

9060

7935

46.7

49

Mondeo

2

16995

9824

7171

42.2

50

Mondeo

3

16995

8361

8634

50.8

From this we can construct a graph, which looks incredibly similar to that of mileage. The line of best fit (trend line) is almost at exactly the same as that of mileage so there is not only an obvious positive correlation with price. This means that as the age increases, the price depreciates more and more, meaning that the overall price will go down.

Age and Mileage

To examine closer the possible similarities between the mileage and the age of the car I have taken 50 cars from my original data to compare their mileage and age as shown below:

 Car Make Model Age Mileage 1 Ford Orion 1 7000 2 Mercedes A140 Classic 1 14000 3 Vauxhall Vectra 2 20000 4 Vauxhall Astra 4 30000 5 Nissan Micra 3 37000 6 Renault Megane 4 33000 7 Mitsubishi Carisma GDI 2 24000 8 Rover 623 Gsi 4 30000 9 Renault Megane 3 41000 10 Vauxhall Tigra 4 27000 11 Fiat Bravo 5 51000 12 Vauxhall Vectra 4 49000 13 BMW 525i SE 8 55000 14 Vauxhall Corsa 2 24000 15 Fiat Punto 4 31000 16 Rover 820 SLi 6 51000 17 Mitsubishi Carisma 2 33000 18 Fiat Cinquecento 6 20000 19 Rover 416i 6 49000 20 Nissan Micra 8 47000 21 Daewoo Lanos 3 42000 22 Rover 114 Sli 6 33000 23 Ford Escort 7 68000 24 Fiat Uno 8 51000 25 Rover Metro 7 43000 26 Vauxhall Nova 10 75000 27 Toyota Corrolla 2 25000 28 Vauxhall Cavalier 10 73000 69 Rover Club 1 2000 30 Volkswagen Golf 7 49000 31 Seat Ibiza 7 45000 32 Rover 214i 8 55000 33 Ford Fiesta 8 90000 34 Fiat Tempra 6 81000 35 Ford Fiesta 11 74000 36 Hyundai Sonnata 9 65000 37 Renault Clio 8 47000 38 Citroen Debut 7 50000 39 Renault Clio 9 98000 40 Fiat Tipo 7 32000 41 BMW 316i 6 71000 92 Volkswagen Polo 5 50000 43 Ford Fiesta LX 7 60000 44 Nissan Micra 9 40000 45 Ford Escort Duet 7 64000 46 Nissan Sunny 7 41000 47 Vauxhall Astra 6 58000 48 Hyundai Accent 6 49000 49 Daewoo Nubira 4 14730 50 Daewoo Lanos 3 32400

Here we can clearly see there is a positive correlation between mileage and price. However, there appear to be many anomalous, or freak, results. The reason for this is due to the fact every car owner does not do the same number of miles per year; while some may only drive 200 miles in a year others may use the car constantly. This means that we cannot hope to get a perfect correlation, but it does show us a clear link between the two.

We can see from the graph that every year around 6100 miles is done, which is slightly lower than expected.

We can take the relationship further by saying that rather than mileage and age being factors with a correlation, we can say that age actually has little to do with price depreciation, and it is actually mileage which reduces the price of the car. We know this as there is a wide spread of results for each age, and mileage correlates almost perfectly with price, so this means that mileage will increase by an average amount each year, and this will affect price, rather than age.

This means that a two year old car which has done a low mileage may be worth the same amount as a two year old car which has done a high mileage,

From this we can now draw further conclusions that mileage and age are clearly linked, and now we can try to work out a formula that combines both mileage and age, as there appears to be a correlation.

Examining make and price depreciation per year

If we take the formula for overall price depreciation, and divide it by the number of years that the car has been used for, we get the percentage price depreciation per year – in other words, the amount the car depreciates every year.

This is very useful as it does not so much give an indication of the mileage or age of the car, but more of the value of the car itself from the original price. Here I have taken around 90 of the cars from the given list, all different makes, and found the depreciation per year for each. Only makes with more than 1 car in the list were chosen so a trend line can be made.

 Make Original price Depreciation per year BMW 28210 9.8 BMW 13650 8.1 Citroen 5715 10.5 Citroen 7680 13.9 Citroen 14065 10.3 Daewoo 11225 15.5 Daewoo 13850 12.6 Daewoo 9525 18.0 Fiat 6864 9.8 Fiat 10423 14.6 Fiat 8272 11.7 Fiat 7864 14.3 Fiat 10954 38.0 Fiat 10810 26.9 Fiat 7518 12.5
 Fiat 10351 13.2
 Fiat 8601 13.4 Fiat 6009 11.1 Ford 16000 50 Ford 8785 11.7 Ford 7875 7.4 Ford 8748 11 Ford 9105 10.7 Ford 12125 21.5 Ford 11800 12 Ford 8680 15.8 Ford 14505 19.7 Ford 13230 12.5 Ford 13183 10.5 Ford 17780 13.8 Ford 6590 7.5 Ford 15405 14.8 Ford 7310 10.7 Ford 9995 11.7 Hyundai 11598 10 Hyundai 6899 9.9 Mercedes 14425 23.8 Mercedes 26425 16.9 Mercedes 17915 17.2 Mitsubishi 14875 29.8 Mitsubishi 15800 31 Nissan 7995 16.7 Nissan 6295 8.9 Nissan 5340 7.8 Nissan 7799 9.5 Nissan 12590 16.5 Nissan 13355 9 Peugot 13975 19.5 Peugot 9125 17.8 Peugot 17490 57.1 Peugot 7600 8.4 Peugot 12350 11.3 Renault 13610 15.8 Renault 13175 15.6 Renault 6795 8.8 Renault 7403 8.9 Renault 11695 12.8 Rover 22980 17.4 Rover 21586 13.7 Rover 13586 12 Rover 8595 11.8 Rover 6645 12.4 Rover 9565 10.3 Rover 24086 17.5 Rover 17795 16.2 Rover 19530 23.2 Rover 24086 14.6 Rover 5495 9.1 Rover 14486 12.4 Vauxhall 18580 28.5 Vauxhall 14325 13.5 Vauxhall 13510 11.1 Vauxhall 18140 16 Vauxhall 8900 21.9 Vauxhall 5599 8.2 Vauxhall 13740 13.1 Vauxhall 7840 9.1 Vauxhall 7440 8.8 Vauxhall 18675 10.4 Vauxhall 9795 11.2 Vauxhall 13435 12.6 Vauxhall 10150 9.2 Volkswagen 9524 8.7 Volkswagen 12999 12.1 Volkswagen 16139 11.3 Volkswagen 14950 9.7 Volkswagen 9960 24.2 Volkswagen 8710 9.2

Conclusion

I have taken this information and put it into a table, and added a formula that should calculate the depreciation of the car:

 Ref. No Age Original Price Current Price Depreciation (%) Predicted Depreciation (%) 17 1 16995 10255 39.7 =(B2*4)+34.8 21 1 16995 10329 39.2 =(B3*4)+34.8 40 1 16995 10520 38.1 =(B4*4)+34.8 7 2 16995 9927 41.6 =(B5*4)+34.8 30 2 16995 9647 43.2 =(B6*4)+34.8 48 2 16995 9792 42.4 =(B7*4)+34.8 4 3 16995 8880 47.8 =(B8*4)+34.8 8 3 16995 8456 50.2 =(B9*4)+34.8 13 3 16995 9322 45.2 =(B10*4)+34.8 20 3 16995 9588 43.6 =(B11*4)+34.8 41 3 16995 9147 46.2 =(B12*4)+34.8 46 3 16995 9192 45.9 =(B13*4)+34.8 16 4 16995 8772 48.4 =(B14*4)+34.8 23 4 16995 8770 48.4 =(B15*4)+34.8 27 4 16995 8673 49 =(B16*4)+34.8 49 4 16995 7960 53.2 =(B17*4)+34.8 5 5 16995 7904 53.5 =(B18*4)+34.8 10 5 16995 7911 53.5 =(B19*4)+34.8 25 5 16995 8139 52.1 =(B20*4)+34.8 38 5 16995 7774 54.3 =(B21*4)+34.8 43 5 16995 8136 52.1 =(B22*4)+34.8 11 6 16995 7417 56.4 =(B23*4)+34.8 22 6 16995 7419 56.3 =(B24*4)+34.8 35 6 16995 7098 58.2 =(B25*4)+34.8 44 6 16995 7030 58.6 =(B26*4)+34.8

We can now put in the values, and to compare this to the real depreciation, we can examine correlation – while a correlation of 1 is perfect, a correlation of 0 means no correlation at all. I am hoping to get a correlation near to 1, since most the points on the graph are near to the trend line. To get the correlation I have used  the formula “=CORREL(E2:E26,F2:F26)”

 Ref. No Age Original Price Current Price Depreciation (%) Predicted Depreciation (%) 17 1 16995 10255 39.7 38.8 21 1 16995 10329 39.2 38.8 40 1 16995 10520 38.1 38.8 7 2 16995 9927 41.6 42.8 30 2 16995 9647 43.2 42.8 48 2 16995 9792 42.4 42.8 4 3 16995 8880 47.8 46.8 8 3 16995 8456 50.2 46.8 13 3 16995 9322 45.2 46.8 20 3 16995 9588 43.6 46.8 41 3 16995 9147 46.2 46.8 46 3 16995 9192 45.9 46.8 16 4 16995 8772 48.4 50.8 23 4 16995 8770 48.4 50.8 27 4 16995 8673 49 50.8 49 4 16995 7960 53.2 50.8 5 5 16995 7904 53.5 54.8 10 5 16995 7911 53.5 54.8 25 5 16995 8139 52.1 54.8 38 5 16995 7774 54.3 54.8 43 5 16995 8136 52.1 54.8 11 6 16995 7417 56.4 58.8 22 6 16995 7419 56.3 58.8 35 6 16995 7098 58.2 58.8 44 6 16995 7030 58.6 58.8

By using the correlation function, we can see that the correlation is 0.96888002. This is very near 1, only 0.031119976 from perfect. We can clearly see from this that my predictions were good. However, this correlation is not so much an indicator of my prediction, but merely showing the correlation between the line on the graph (which I have used to base my predictions on) and the points on the graph.

Evaluation

In conclusion, given the time constraints I had, I believe that I have been relatively successful in investigating my hypotheses. I have looked into make, age, mileage and also predicted ages of cars (which would almost definitely correlate well with mileage in addition, as the two are linked). Given more time, I could have done investigations into engine size and other such specifications of cars. I could have also represented my data in other forms, such as box plots, etc, and used standard deviation and skewness in my project.

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