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  • Level: GCSE
  • Subject: Maths
  • Word count: 3719

Analyse a given set of data concerning used car sales and investigate the relationship that particular variables have with each other ones.

Extracts from this document...

Introduction

James Black

Used Car Sales

Introduction

The aim of my investigation is to statically analyse a given set of data concerning used car sales and investigate the relationship that particular variables have with each other ones. These are the following variables: -

  • The make of the car
  • The model of the car
  • The price when new
  • The price when second hand
  • The age of the car
  • The colour of the car
  • The car’s engine size
  • The type of fuel the car takes.
  • The MPG (miles per gallon) of the car
  • If the car has been serviced
  • The number of owners

To begin with I will investigate how the age of a vehicle affects the price when being resold and if this varies form make to make.

Prediction 1

From my experience with cars and gained knowledge, I am able to predict that as the age of a car increases the car depreciates and its value is lowered. Concerning the make and model of the car, the age and depreciation rate relationship will differ depending on what car is being looked at, for example a Ford Focus will depreciate at a slower rate than a Ford Escort because it is higher up in the range and more desirable to buyers.

Hypothesis 1

As a vehicle’s age increases the price of that vehicle will decrease.

To aid me in my coursework I was presented with a table of 100 cars and their attributes e.g. colour, make, and age e.t.c. So that everyone’s coursework was different and to make it a little easier I decided to chooses 36 cars out of my given 100 to use as a sample for my study. I chose the number 36 firstly as it is divisible by 360 (number of degrees in a pie chart) and big enough to provide a wide range of contrasting results.

...read more.

Middle

28210

5995

8

white

2.5

unleaded

21-38

55000

yes

3

25

Mercedes

Elegance

26425

17500

2

silver

2

unleaded

25-44

22000

yes

1

26

Renault

19

11695

2748

6

blue

1.9

diesel

39-60

52000

no

2

27

Volkswagen

Beetle

14950

13500

1

silver

2

unleaded

24-41

6500

yes

1

28

Roer

623 GSi

24086

2975

6

blue

2.3

unleaded

25-41

96000

yes

2

29

Suzuki

Vitara

10800

2995

8

red

1.6

unleaded

26-35

50000

no

2

30

Mercedes

AvantGarde

17915

11750

2

silver

1.6

unleaded

28-50

17000

yes

1

31

Peugot

306

12350

3995

6

white

1.9

diesel

40-61

71000

no

2

32

Fiat

Punto

7518

3769

4

blue

1.1

unleaded

36-60

38000

no

2

33

Volkswagen

Polo

8710

4693

5

red

1.4

unleaded

37-59

50000

yes

2

34

Vauxhall

Calibra

18675

6995

6

blue

2

unleaded

27-43

63000

no

2

35

Rover

Metro

5495

1995

7

blue

1.1

unleaded

40-58

52000

no

2

36

Vauxhall

Vectra

13435

4995

5

red

1.8

unleaded

30-52

52000

no

2

When this investigation has been completed I hope to understand a lot more about cars and how they are priced in terms of their characteristics and how mathematics can be applied to everyday situations such as the analysis of used cars.

Initially, I will be comparing the prices of all thirty-six cars with their age. Generally as the age of a car increases it is likely to depreciate in value. Therefore age definitely has an affect on the price of the car.

image00.png

As is visible on the graph as the age of a car increases the price decreases. These findings are in line with my prediction and back up my hypothesis. The graph also shows that a new car will depreciate at a faster rate than that of an older car. Therefore, the price depreciates slower as the age goes up. This graph is also correct in showing that no matter how old a car becomes it will never be worth a negative value.

So, a conclusion can be made from the graph, firstly

  • As the age of a car increase the price decreases.
  • No matter how old the car is its price will never become a negative value.

Prediction 2

Next I will compare the mileage against the current price of the car.

...read more.

Conclusion

Despite having a low mileage the age counts more towards a cars value because depreciation can occur even when the engine is switched off.There is little correlation between a cars mileage and its age.If the results were averaged then the average miles per year travelled by each car produced by any manufacturer would be 8355.7.The current price and engine size have little correlation if any.
  • A larger engine size will result in a more expensive original price for a car.
  • The original price of a car is more or less directly proportional to its engine size on average.
  • For every increase of one litre to the car’s engine size the price increases £10790 in average for all car manufacturers.
  • Strong links do not occur between the current price and original price of a car although some forms of correlation can be made.
  • The rate of depreciation is not constant, because it is affected by many other variables such as the age, mileage, original and current price as well as the engine size.
  • The depreciation rate for a car indicates how much a car loses value (in %) since the previous year. This means the depreciation rate (in percentage changes every year getting smaller each year if all the other variables are either kept at at a constant or made into an average.

I have found this analysis very interesting and after looking and evaluating the evidence I have found the following:

  • Car manufacturer Fiat uses many of the smaller engine sizes in their cars so that their cars are cheaper to run, more economical but slower as a result.
  • Rover and Vauxhall hold their value the longest while producing relatively speedy and efficient cars.
  • Ford produces cars that are expensive to purchase new and depreciate quickly but are fast, technically sound, and fairly efficient.
  • Ford tends to have bigger engine outputs than the other car manufacturers.
  • Fiat produces the cheapest cars when new due to their simple designs.

...read more.

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