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  • Level: GCSE
  • Subject: Maths
  • Word count: 2408

In the maths coursework we have been set, we have been asked to use information provided to investigate what influence the price of a second hand car.

Extracts from this document...

Introduction

Maths coursework

In the maths coursework we have been set, we have been asked to use information provided to investigate what influence the price of a second hand car. The information contains different makes, models, and price when new, price when old, and engine size, fuel, MPG, mileage, service and owners on 100 cars.

During the coursework I will be investigating: -

Introduction:

As part of my GCSE Maths coursework, I have been asked to investigate how the price of a car drops over a certain period of time, depending on certain factors. The cars I will be looking at will be second hand, all the data on these cars will be given to me by my class teacher. I will use the data from this database and compare the data using different methods and calculate how the price of the car drops by each of the certain factors.

Aim:

As part of my coursework I will gather and collect the data I will require from the database on the cars that will be using in my investigation. I will use this data then and place them into tables and then later on draw them into graphs, which I will then use to calculate how the price of the cars drop depending on the certain factors. I will use graphs such as bar graphs, pie charts and even scatter diagram to present my data.

...read more.

Middle

3

Astra= 28*3=84

Tigra

|

1

Tigra= 28*1=28

Corsa

|||

3

Corsa=28*3=84

Nova

|

1

Nova=28*1=28

Cavalier

|

1

Cavalier=28*1=28

Calibra

|

1

Calibra =28*1=28

This data will be on a pie chart, I will find the angle by divided the total number of cars by 360, as 360 is the total angle of a whole circle.

360/13=28

Now I have to times 28 by the number of cars.

A pie chart to show the

Number of Vauxhall models

image16.png

This same information will then be put on a graph.

A bar graph to show

The number of Vauxhall models

image17.png

The third type of car chosen was Nissan

Type of model

Tally

Frequency

Angle

Micra

||

2

360/5*2=144

Sunny

|

1

360/5*1=72

Primera

|

1

360/5*1=72

Almera

|

1

360/5*1=72

A pie chart to show

The number of Nissan models

image18.png

The pie chart shows that there are more models of Micra then any other models associated with Nissan. The pie chart also shows that there are an equal number of the remaining models.

The same information will be shown on a bar graph.

 A bar graph to show

The number of Nissan models

image19.png

A scatter diagram showing the Used Price of the car against its age in years:

Now, i am going to investigate the age that effects on the used price for the different makes.

Used Price (£)

Age (yrs)

7999

1

1595

7

1050

8

1495

11

1995

7

2300

7

4295

3

4700

5

3200

4

8800

2

8250

3

3495

7

7995

4

1664

10

3995

5

2995

6

image02.png

Looking at the scatter diagram above I can say as the older the car was the less it costs to buy, I can say the graph showed a negative correlation.

The next ten cars chosen at random for negative correlation was Vauxhall-Cavalier, Volkswagen-Golf, Renault-Clio, Fiat-Punto, Nissan-Micra, Bmw-316i, Daewoo-Lanos, Ford-Orion, Ford Fiesta and Mitsubshi-Carisma.

Car

Age

Price

Vauxhall-Cavalier

10

£850

Volkswagen-Golf

15

£400

Renault-Clio

9

£1495

Fiat-Punto

4

£3995

Fiat-bravo

5

£3495

Bmw-316i

6

£6995

Daewoo-Lanos

3

£5999

Ford-Orion

1

£7999

Ford Fiesta

8

£1050

Mitsubshi-Carisma.

2

£5999

This information will then be put onto a scatter diagram.

image03.png

This scatter diagram shows that as the car gets older in age the price will also drop, this type of scatter diagram has negative correlation.

The next set of car chosen at random was;

Car  

 Used Price

 Age

Rover-Metro

£875

7

Ford-Fiesta

£1050

8

Hyundai-Accent

£2800

6

Seat-Ibiza

£795

7

Fiat-Bravo

£4995

2

Honda-Civic

£7995

1

Nissan-Almera

£4300

4

Vauxhall-Vectra

£4995

5

Peugeot-406LX

£5795

3

Rolls-Royce-Silver Spirit

£14735

9

image04.png

From the graph we can see that as the car gets older the price will depreciate, depending on how expensive the car is, for example the car on the graph is 9 years old and is still selling for £14,500.

This graph is negative correlation.

The next ten cars chosen at random for negative correlation was Vauxhall-Cavalier, Volkswagen-Golf, Renault-Clio, Fiat-Punto, Nissan-Micra, Bmw-316i, Daewoo-Lanos, Ford-Orion, Ford Fiesta and Mitsubshi-Carisma.

Car

Age

Price

Vauxhall-Cavalier

10

£850

Volkswagen-Golf

15

£400

Renault-Clio

9

£1495

Fiat-Punto

4

£3995

Fiat-bravo

5

£3495

Bmw-316i

6

£6995

Daewoo-Lanos

3

£5999

Ford-Orion

1

£7999

Ford Fiesta

8

£1050

Mitsubshi-Carisma.

2

£5999

...read more.

Conclusion

td class="c27" colspan="1" rowspan="1">

Price

Bmw- 316i

6

£6995

Vauxhall-Astra

4

£6595

Fiat-Bravo

5

£3495

Vauxhall-Cavalier

10

£850

Ford-Fiesta

11

£1495

Nissan-Micra

8

£1795

Daewoo-Lanos

3

£4395

Ford-Escort

7

£1595

Nissan Primera

9

£2574

Landrover-Discovery

1

£13995

image06.png

This correlation graph also shows negative correlation.

A scatter diagram showing the old Price of a car against its Mileage:

Price (£)

Mileage

16000

7000

8785

68000

7310

90000

7875

74000

8748

60000

9105

6400

12125

29000

11800

34000

8680

27000

14505

7200

13230

34000

13183

43000

17780

30000

6590

37000

15405

57000

9995

64000

image07.png

From the scatter diagram above there is no correlation, this would mean that that the old Price of a car and its Mileage are not related to one another and have no affect on each other.

The next cars chosen to use against no correlation were;

Car (ford)

Used Price

Mileage

Ford Orion

£7999

7000

Ford Escort

£1595

68000

Ford Fiesta

£1050

90000

Ford Escort Duet

£2300

64000

Ford Focus

£8800

7200

Ford Puma

£8250

34000

Ford Mondeo

£7995

30000

Ford-Escort

£13183

43000

image08.png

This graph no correlation, the reason why it show no correlation is because the price and the mileage of the car have no relation with each other.

The next set of cars chosen was;

Car (Rover)

Used Price

Mileage

Rover-623 GSi

£6999

30000

Rover-820 SLi

£3795

51000

Rover-416i

£3795

49000

Rover-114 Sli

£2495

33000

Rover-Metro

£895

43000

Rover-623GSi

£2975

96000

Rover-620Si

£3400

66000

image09.png

The last set of cars chosen was;

Car

Used Price

Mileage

Volkswagen-Golf

£3695

49000

Volkswagen-Golf

£3595

58000

Volkswagen Golf Gti

£6995

35000

Volkswagen-Beetle

£13500

6500

Volkswagen-Polo

£7550

5000

Volkswagen-Polo

£4693

50000

This scatter graph shows no correlation.

image10.png

Cumulative frequency

 Cumulative frequency means “adding it up as you go along”.

the following on the table shows the cumulative frequency.

Price  

Frequency

Mid interval (£)

Cumulative frequency

0<10,000

7

5000

7

10,000<20,000

6

15000

13

20,000<30,000

9

25000

22

30,000<40,000

11

35000

33

40,000<50,000

18

45000

51

50,000<60,000

17

55000

68

60,000<70,000

7

65000

75

image11.png

Inter quartile= upper quartile- lower quartile

Upper quartile =3/4 (n+1)

Upper quartile = ¾ (75+1)

                        = ¾ (76)

                        = ¾ *76

                        = 228/4

                       = 57

Lower quartile = ¼ (n+1)

                        = ¼ (75+1)

                        = ¼ (76)

                        = ¼ * 76

                        = 19

Inter quartile = 57- 19

                     = 38

Price  

Frequency

Cumulative frequency

0<20,000

20,000<40,000

40,000<60,000

60,000<80,000

80,000<100,000

...read more.

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