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  • Level: GCSE
  • Subject: Maths
  • Word count: 2935

Use the information to investigate what influences the price of cars.

Extracts from this document...

Introduction

Andrew Frampton

Wilson’s School

Guaranteed 18/24 on Higher Tier

GCSE Coursework 2002/2003

Mathematics

Use the information to investigate what influences the price of cars.

Objectives

  1. Specify clearly what you plan to do and why you are approaching the data in this way.
  1. Collate the data needed and represent it in a way, which helps to develop the investigation.
  1. Interpret the results and draw conclusions from them.

Each of these strands is worth a possible 8 marks.

The source of all my data is a printed database of cars which was issued to everybody doing the investigation. It includes various fields, some of which will be used in my investigation. They are:

  • Car make
  • Car model
  • Price when new
  • Price now
  • Age
  • Colour
  • Engine size
  • Fuel
  • Miles per gallon
  • Mileage
  • Service
  • Owners
  • Length of MOT
  • Tax
  • Insurance
  • Doors
  • Style
  • Central Locking
  • Seats
  • Gearbox
  • Air conditioning
  • Airbags

Objective 1

Specify clearly what you plan to do and why you are approaching the data in this way.

Aim

My aim is to find out exactly what factor affects the price of second hand cars most.

What I plan to do

I plan to use a series of hypotheses and test them against the data to see if they affect the price of second hand cars. I will do this by predicting three hypotheses of my choice, which are relevant to the data.

I will use an example from every make of car for each hypothesis. To avoid bias I will variate in where I select the car from on the sheet e.g. at the very beginning or at the end.

...read more.

Middle

3

9

6

6250

11

5

25

7

3999

18

11

121

8

2975

21

13

169

9

4999

16

7

49

10

5795

15

5

25

11

5999

13

2

4

12

6999

10

-2

4

13

5995

14

1

1

14

7995

9

-5

25

15

5999

13

-2

4

16

13995

4

-12

144

17

7495

9

-8

64

18

19495

2

-16

256

19

795

25

6

36

20

2995

20

0

0

21

1195

24

3

9

22

3995

19

-3

9

23

1495

23

0

0

24

2495

22

-2

4

25

14735

3

-22

484

Total

1665

I drew up a table like this so we could easily work out the Spearman’s Rank Correlation Coefficient for the data. The table has the fields rank, price, rank, difference and difference² as all of these components are needed to complete the formula for it. It will tell us whether there is a positive or negative correlation between the data.

Table 2

Price (£)

Cumulative Frequency

0 up to but not including 4000

8

0 up to but not including 8000

20

0 up to but not including 12000

21

0 up to but not including 16000

23

0 up to but not including 20000

24

0 up to but not including 24000

24

0 up to but not including 28000

24

0 up to but not including 32000

24

0 up to but not including 36000

24

0 up to but not including 40000

25

I drew up another table like this (above) so that calculating the cumulative frequency for the data would be easy. It allows us to draw up a graph to show the data.

Graph 3

image02.png

I chose to put a cumulative frequency graph in so that we could see how the data works in proportion with one another. I set the graph out like this as it is the clearest and simplest way to produce data in this form. We expect to see a continuous rise in the graph.

Statement 2: The price of second hand cars will increase with engine size.

...read more.

Conclusion

I conclude that again, in this hypothesis also, that the engine size of the car does affect its second hand price.

Statement 3:The price of second hand cars will decrease with the mileage it has done.

Graph 1

In this graph I saw that that in general there was no relationship between the price now and the mileage it had. Most of the time, when the prices now increased so did the mileage, completely contradicting my hypothesis. This may be because people do not mind how much mileage a car has so the car dealerships can exploit this by raising the prices of older cars with a lot of mileage. Another reason may be because the cars with the most mileage may have only had one previous owner, was not very old or had a small engine. All of these factors may have influenced the prices of cars further.

I conclude that in this hypothesis the mileage did not have a significant effect on the price of the cars.

In general I saw that only two of my hypotheses were correct out of a possible three. Out of the two which were correct and did affect the price of second hand cars as I had expected, I believe that the one which had the most influence on the price of second hand cars was age. This is because we saw the most significant relationships between price and age in this graph than in the engine size graph.

...read more.

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