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  • Level: GCSE
  • Subject: Maths
  • Word count: 3699

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

Extracts from this document...

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.

...read more.

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

...read more.

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

                                                                         16                

-------------------------------------------------------------------------------------------------------                                

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

image05.png

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

image06.png

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

-------------------------------------------------------------------------------------------------------

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.

image07.png

image08.png

image09.png

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%.

image10.png

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.

...read more.

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