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  • Level: GCSE
  • Subject: Maths
  • Word count: 3172

Used Car Prices

Extracts from this document...

Introduction

Vina Ragupathy 11L

Maths Coursework
Used Car Prices

There are many factors that will strongly affect the price of a used car, such as the:

  • make
  • age
  • engine size
  • condition of the car
  • mileage
  • type of fuel used
  • number of previous owners

Plan

I plan to investigate how mileage, engine size and age of the car will affect the second-hand selling price of a used car, as I believe that these are the most important factors that will have the greatest effect on the price.

  • Firstly, I will analyse the data we have been given in the appendix.
  • I will input this data on to a spreadsheet to aid my analysis.
  • Using the ‘Auto Filter’ function I will group cars under their make, enabling for a fair comparison to be made between the price and the factors that will affect price.
  • I will produce scatter graphs which will display the results in such a way that a trend can be spotted easily.
  • From these trends I will make a few simple hypotheses, stating what I would expect to find from examining a different set of data
  • To test these hypotheses I will use external resources such as car magazines, which contain a listing of used cars and their mileage, engine size and age, thus enabling me to obtain a wider range of the data I require. A sample size of approximately 50 cars would be sufficient for investigation.
  • I will use random sampling to obtain my data set to remove bias from my collection; this would also be a better test of my predictions. To do this, I will either select 1 in every 5 cars or use the random number generator on my calculator.
  • Once I have gathered my data set I will set about processing it and representing it in the forms of charts and graphs. I could use scatter diagrams again, which would make it an easier comparison to my initial set of results. Alternatively I could use a cumulative frequency graph which will also help me find the median and inter-quartile range.
  • After I have collated the data I will try and find a general formula for the depreciation of car prices.
  • I will then set about refining my investigation to find a more accurate formula. I can do this by concentrating on a specific type or model of car or maybe even combining some of the features.
  • The final stage of my investigation will be to write up a conclusion describing my findings.
...read more.

Middle

image04.png

There is quite a strong negative correlation here, apart from a couple of points where two different cars have a difference of 20000 for the mileage but are priced the same. The gradient of the graph = -£4000 ÷ 60000miles = £666.67 average depreciation per 10,000miles travelled.

image05.png

For the above graph there is almost perfect negative correlation. This is the strongest indication yet that age is a very important determinant of price. The gradient of the graph is approximately -£3000 ÷ 5 years = £600 average depreciation per year, which is relatively low and would attract buyers as it may be seen as an investment to buy the car.

image06.png

There is absolutely no correlation once again between engine size and price.

Volkswagen is another of the populous makes of car. Here I will analyse the graphs I have produced from the data I gathered from the appendix.

image07.png

There is a visible negative correlation between mileage and selling price in the graph above, even though there are only 6 cars whose data has been used. Besides one, the points do not vary much from the line so we can say that the graph is strongly correlating. The results displayed add further emphasis to the idea that mileage influences price.

image08.png

I cannot say that there is much correlation in the above scatter diagram, probably because there are not enough cars to establish any pattern in this case. However a line of best fit can still be drawn if we disregard the outlying point.

The gradient of this line is approximately -£4000 = average depreciation of £500 / year.                                                       8 years

This is a very cheap average depreciation but under similar circumstances to a previous analysis of another make of car, I have disregarded an outlying point.

...read more.

Conclusion

y     1

       x

y =  k

       x

when x is 15000, y is 6000 => 6000 =     k   s

             15000

                                => k = 6000 x 15000s= 90,000,000

therefore, the final equation is y = 90,000,000

               x

However, the values used in this calculation were estimations taken from the computer drawn graph which you see displayed above, and so the actual formula may differ slightly from what I have been able to work out.

image11.png

There is some negative correlation in the graph above, although there is no strong, definite pattern. This still proves my hypothesis that “The more expensive cars…will be younger in age.” We can still use the graph to obtain a general formula for the average depreciation per year of these cars:

y = mx + c → m = gradient, c = y-intercept

gradient = £4000 - £6000        = -2000        = - 800

               6yrs – 3.5yrs              2.5                       1

y-intercept ≈ £9000

if we take the point (6,4000), x = 6, y = 4000

substitute into y = mx + c → 4000 = -800x6 + 9000

                                   4000 = -4800 + 9000

                                 -5000 ≈ -4800

Once again the formula was created using estimated figures, and so it is acceptable that when checking the values for the formula the answers were only approximately the same.

Therefore, we can establish the formula for average annual depreciation as:

y = -800‘x’ + 9000 (‘x’ denotes x as a letter rather than a multiplication symbol)

image13.png

It is clear that there is no correlation between the engine size and the price of a car, suggesting that although it may appear to be quite an important factor, it does not influence the price as much as other factors such as mileage and age. In this sense, this proved my prediction that “cars with larger engine sizes will be more expensive than cars with small ones” to be incorrect, as we can clearly see that some cars have smaller engines yet are more expensive than cars with larger engines.

        -  -

...read more.

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