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Second Hand Car Prices

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Introduction

Page  of         Mohammed Ramji

image00.png

SUMMER 2002

SECOND HAND CAR PRICES

Hypothesis

THE VALUE OF A USED CAR DECREASES EXPONENTIALLY WITH ITS AGE.

Byexponentially it means that a graph of a certain make of car, its price on one axis and its age on the other, would show a curved decrease in price over a period of time as shown in the example on the following page.

The following experiment is being conducted to help and assist people who are buying and selling cars in magazines such as “Auto Trader”.

Approach

Throughout the project I have referred to the second hand car sales pages in the magazines “Auto Trader” and “Exchange & Mart” (in the local paper) for data. In these, I found a wide range of data over three weeks from which to select the type of data required. I selected relevant pieces of data in each age range for the Mercedes C-Class. If there was not enough information in the source I would have referred to another car magazine. Due to the fact that sampling concentrates on gaining information about selected sampling units, the quality of information gained is better than if the information was of units that had not been specified.

...read more.

Middle

Age

Average Car Price

0

31,995

1

22,696

2

14,449

3

11,299

4

8,713

5

11,421

6

7,147

7

5,646

8image04.png

4,730

I used standard deviation to explain the average spread of the values from the mean for each year.

Example of SD

KEY

∑x

SUM OF ALL VALUES

n

NUMBER OF VALUES

∑x2

SUM OF ALL SQUARED VALUES

x

(x-x)

(x-x)2

5

-0.2

0.04

∑(x-x)2

 = 48.8

7

1.8

3.24

n

5

3

-2.2

4.84

9.76

10

4.8

23.04

1

-4.2

17.64

∑(x-x)2

 = 3.124

n

∑x=26

∑(x-x)=0

∑(x-x)2=48.8

n=5

x=∑x/n

x=5.2

ACTUAL MERCEDES DATA ANALYSED IN THE FORM OF STANDARD DEVIATION

Year

N

∑x

x

∑x2

SD

0

2

63990

31995

2047360050

0

1

4

90784

22696

2063508076

876.7

2

6

86694

14449

1276816606

2007.3

3

9

101691

11299

1166946609

1411.9

4

14

121982

8713

1116024038

1949.3

5

4

45684

11421

526881076

1131.8

6

4

28588

7147

207733252

924 .0

7

4

22584

5646

128502076

498.2

8

3

14190

4730

67277251

236.7

The results gathered from the standard deviation information show that the spread of all the plotted figures is fairly small. This is also the case for the fifth year in the Mercedes car data, which means that even though the results are out of line, the plotted data is close together within a small price range.

Analysis

As seen in

...read more.

Conclusion

        The results shown above would have been more accurate if the same number of data points were available in each ‘year group’, and this would give a more accurate mean. This was noticed and the data for the VW Golf GTI was adjusted accordingly to see if there was any significant data. There may well have been, but more data points would have to be available for each year range.

The results for the VW Golf GTI show that, with fewer data points for each range, the standard deviation tends to be lower. This implies greater accuracy, but a greater range of points may show that this is not the case. On the other hand, the limitations of the data would improve the level of accuracy.

Also, all the data used is from two particular types of newspaper/magazine. Not everyone who has a Mercedes C-Class to sell decides to advertise in these particular publications. Therefore, if I were to repeat the experiment or develop it further, I would have to take into consideration data from other newspapers/magazines.

Using spearman’s rank may produce a more accurate line of best fit. If there was more time to conduct this experiment, I would have investigated this area.

...read more.

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