# The aim of our coursework is to investigate the effect of different variables on the price of a second hand car.

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Introduction

Hugh Williams

Investigation

Aim:

The aim of our coursework is to investigate the effect of different variables on the price of a second hand car. I will try and achieve this aim by setting three hypotheses that I will try to prove or disprove depending on the results of the test data. In order to test the data I will be using sampling techniques to chose a sample that I will be working with throughout the investigation.

Hypotheses

- I predict that the depreciation of a used car depends on its age. This is because as a car increases in age it becomes less desirable and depreciates more in price. I expect there to be a positive correlation between age and percentage decrease in price.

- I predict that the price of a used Vauxhall is dependant on engine size. This is because as a car’s engine size increases, the car becomes more desirable and enters higher price brackets. The increase in engine size often leads to an increase in specifications as well which in turn leads to a slower depreciation rate. I expect there to be a negative correlation between engine size and percentage decrease in price.

- I predict that the price of a used car is dependant on mileage. This is because as the mileage of a car increases, the car becomes less desirable.

Middle

17195

11750

2

5445

31.67

17000

98

Renault 19

11695

2748

6

8947

76.50

52000

17

Mitsubishi Carisma

15800

5999

2

9801

62.03

33000

41

BMW 316i

13650

6995

6

6655

48.75

71000

21

Daewoo Lanos

11225

5999

3

5226

46.56

42000

48

Hyundai Accent

6899

2800

6

4099

59.41

49000

88

Citroen Xantia

14065

2450

8

11615

82.58

49000

90

Peugot 306

12350

3995

6

8355

67.65

71000

In order to prove or disprove my first hypothesis “I predict that the depreciation of a used car depends on its age.” I will be using the stratified selective sample that I have outlined above. The advantage of using a stratified sample is that it minimises the amount of bias in the sample.

Age | Cumulative Frequency |

1 | 0 |

2 | 3 |

3 | 4 |

4 | 6 |

5 | 10 |

6 | 18 |

7 | 21 |

8 | 22 |

9 | 24 |

10 | 24 |

11 | 25 |

The graph shows the effect age has on the percentage decrease in price of a car. The results show that age has a large effect on the prices of second hand cars. With an increase in age the decrease in price as a percentage also increases. For example the Mercedes AvantGarde has a percentage decrease in price of just 31.67% whereas the Fiat Tempra has a decrease of 87.58%. This is due to the fact that the Mercedes is only 2 years old and the Fiat is 6 years old. This is reflected in the graph by a very strong positive correlation between the data. This suggests that the older a car gets, the greater its percentage decrease.

The mean age is 5.72; this was calculated by adding the age values together and dividing by the size of the sample.

The modal age is 6 as this is the age value that occurs most often in the data, eight times in total.

The median age is 6.5 as this is the middle value when the data is arranged in order of size.

The spread of data is 10 as this is the number of different ages in the sample.

Median | Lower Quartile | Upper Quartile | Interquartile Range |

6.5 | 4.1 | 6.2 | 2.1 |

Conclusion

The mean mileage is 1169000/25 = 46760.

The modal mileage is 49000 as this occurs most often, five times in total.

The median mileage is 49500.

Mileage | Cumulative Frequency |

0-10000 | 0 |

10001-20000 | 2 |

20001-30000 | 3 |

30001-40000 | 7 |

40001-50000 | 14 |

50001-60000 | 19 |

60001-70000 | 21 |

70001-80000 | 24 |

80001-90000 | 25 |

90001-100000 | 25 |

Median | Lower Quartile | Upper Quartile | Interquartile Range |

49500 | 39000 | 59500 | 20500 |

From the Box and Whisker diagram we can see that the data is very evenly spread. The inter quartile range is relatively small. This suggests that the data is tightly concentrated around the median.

From the above results I can conclude that my hypothesis was correct. The price of a second hand car depends on its mileage. As the mileage of a second hand car increases, the percentage decrease in price of the car also increases. This can be explained by the fact that as a car’s mileage increases so does its age. As already shown above, age has a large impact on the price of a second hand car. Also as a car’s mileage increases so does the wear and tear on the car. This can lead to expensive repairs and may affect the length of the MOT history.

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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