# The aim of this coursework is to find out what affects the price of a second hand car.

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Introduction

Maths Coursework: Data Handling.

### By Gurpreet Bhamra. 11W1

AIM: The aim of this coursework is to find out what affects the price of a second hand car

INTRODUCTION: In this investigation I have been given a set of data of 100 cars, from which I have to investigate the factors that affect a second hand car. The data includes information such as; model, make, colour, mileage, number of previous owners, etc… From this data I will only use 30% of it, and I will put I a certain amount of cars from my own research so I have a fair representation of the population. The 30% can be chosen by two methods, either by Stratified sampling (which is when the population is divided into categories, and then a random sample is taken from each category. The size of the sample is in proportion to the size of the data, as in if there is 10 cars in a group, at least 30% will be chosen so its fair). Another method is by Systematic Sampling, which is when a regular pattern is used in choosing the sample. The initial point is randomly chosen and then the nth term selected thereafter. Another method is by random Sampling, which can be done using a calculator or by putting values into a hat or bucket and picking at random. On the calculator, it can be done by pressing, “shift” “ran#” and “=”. The value given will have to be rounded off to either 1 or 2 decimal places.

Middle

1 Ford Orion 16000 7999 1 black 1.8

4 Vauxhal Astra 14325 6595 4 black 1.6

11 Fiat Bravo 10351 3495 5 red 1.4

16 Rover 820 SLi 21586 3795 6 red 2

17 Mitsubishi Carisma 15800 5999 2 blue 1.8

19 Rover 416i 13586 3795 6 silver 1.6

25 Rover Metro 6645 895 7 Nightfire 1.1

29 Volkswagen Golf 400 15 green 1.4

35 Ford Fiesta 7875 1495 11 red 1.8

38 Citroen Debut 5715 1495 7 black 0.95

39 Renault Clio 7403 1495 9 red 1.2

47 Vauxhall Astra 13740 2900 6 blue 1.6

49 Daewoo Nubira 13850 6895 4 black 2

52 Ford Escort 12125 4295 3 white 1.4

56 Lexus LS400 39728 6250 7 blue 4

60 Rover 620Si 17795 3400 5 blue 2

64 Ford Focus 14505 8800 2 black 1.6

67 Peugeot 406 17490 7500 1 silver 2

68 Honda Civic 12895 7995 1 green 1.4

69 Rover Club 19530 14999 1 grey 1.8

70 Fiat Bravo 10810 4995 2 green 1.4

73 Porche Sport 32995 19495 6 silver 3

77 Mercedes AvantGarde 17915 11750 2 silver 1.6

79 Volkswagen Polo 9960 7550 1 blue 1.4

80 Ford Escort 13183 3495 7 red 1.8

82 Mazda Pegasus 10420 2495 7 green 1.3

85 Vauxhall Corsa 7440 3495 6 green 1.2

89 Peugeot Graduate 7600 2497 8 red 1400

93 Vauxhall Calibre 18675 6995 6 blue 2

98 Renault 19 11695 2748 6 blue 1.9

The following cars were chosen (can be seen above):

LOSS OF VALUE:

For each car in my sample, I need to work out the depreciationof it. This is found out by, the following formula:

## Original value – New value = difference in value

## Difference in value X 100 = percentage of depreciation

## Original value

For example: for the first car, which’s data has been given below:

Car no make model price (new) _ price (second hand).

1 Ford Orion 16000 7999

So the value is found out like this:

- 1600 – 7999 = 8001

- 8001 / 16000 X 100 = 50%

From the following table, you can see the depreciation values for all 30 cars:

Depreciation ranges:

Car no: | Make and model | New price | Old price | Depreciation: | Percent: |

1 | Ford Orion | £16000 | £7999 | 16000 - 7999 = 8001 X 100 16000 | = 50% |

4 | Vauxhall Astra | £14325 | £6595 | 14325 - 6595 = 7730 X 100 14325 | = 54% |

11 | Fiat Bravo | £10351 | £3495 | 10351 – 3495 = 6856 X 100 10351 | = 66.2% |

16 | Rover 820SLi | £21586 | £3795 | 21586 – 3795 = 17791 X 100 21586 | = 82.49 = 83% |

17 |

Conclusion

The range is 8800 – 1050 = 7750

The average age for Fords is:

7 + 3 + 5 + 7 + 5 + 6 + 7 + 8 + 4 + 10 + 7 + 2 + 4 + 1 + 3 + 11 = 79 = 4.93 = 5 years

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Now I am going to do a cumulative frequency diagram for the Vauxhall ages. These are the ages for Vauxhalls,

I will put this in a table now:

AGE | TALLY | FREQUENCY | C.F |

1 | 0 | 0 | 0 |

2 | II | 2 | 2 |

3 | 0 | 0 | 2 |

4 | IIII | 4 | 6 |

5 | I | 1 | 7 |

6 | IIII | 4 | 11 |

7 | 0 | 0 | 11 |

8 | 0 | 0 | 11 |

9 | 0 | 0 | 11 |

10 | II | 2 | 13 |

TOTAL | 13 | 13 |

From the above graph, you can see that overall the car prices rose slowly, steadying twice which could be due to no cars actually falling in between this numbers. The median is 13 + 1 = 14 / 2 = 7, so it’s the 7th position, which is about 5. The range for this data is 9, (10 – 2 = 8), the lower quartile is 3.25, and the upper quartile is 9.75. The inter-quartile range is 9.75 – 3.25 = 6.5. Below you can see a box plot for this cumulative frequency graph.

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VAUXHALLS: the average price for Vauxhall cars was found in the same way as above.

6595 + 2900 + 3191 + 6995 + 850 + 4995 + 4976 + 3495 + 1000 + 7499 + 7999 + 6499 + 4995 = 61989 = 4768.3 = 4768

13

The median is 4995. (The 7th value)

The range is 7999 - 850 =7149

The average age for Vauxhalls is:

4 + 6 + 6 + 6 + 10 + 2 + 4 + 6 + 10 + 4 + 2 + 4 + 5 = 69 = 5. 3 years which is 5 years

13

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Box plots:

From these box plots I can tell that

FURTHER INVESTIGATION:

Now I am going to look at just one make which I have chosen to be Vauxhall, and I will choose three models, which will be Astra , Corsa and Vectra. I will compare these to see which of this decrease the quickest.

The average depreciation price for Astra is the following:

- 14325 – 6595= 7730 / 14325 X 100= 54%

- 13740 – 2900 = 10840 / 13740 X 100=79%

- 9795 – 3191 = 6604 / 9795 X 100 = 67%

67 + 79 + 54 = 200 / 3 = 66.8 = 67%

The average depreciation price for Vectra is:

- 18580 – 7999 = 10581 / 18580 X 100 = 56.9 = 57%

- 18140 – 6499 = 11641 / 18140 X 100 = 64%

- 13435 – 4995 = 8440 / 13435 X 100 =62.8 = 63%

57 + 64 + 63 = 184 / 3 = 61.3 = 61%

The average Depreciation price for Corsa is:

- 8995 – 4995 = 4000 / 8995 X 100 = 44.5 = 45%

- 7840 – 4976 = 2864 / 7840 X 100 = 36.5 = 36%

- 7440 – 3495 = 3945 / 7440 X 100 = 53%

45 + 36 + 53 = 134 / 3 = 44.6% = 45%

So from this you can see that the Vauxhall Corsa depreciates the least amount with 45%, while the Vauxhall Astra depreciates the most with 67%.

From this you can tell that age is a major contributing factor that affects the price of a second hand car, as well as mileage.

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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