Used Car Prices

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                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.

Investigation

I used the filter function on the spreadsheet to form scatter diagrams comparing mileage with price, engine size with price, and age with depreciation. After producing a pivot table on Excel, showing the numbers of cars in the database for each make of car, I decided to begin by analysing the data for all Ford cars, as this was the most populous make of car from the appendix.

From this scatter diagram you can see that the car with the highest mileage has the lowest price, and the cars with the lowest mileage have the highest prices. Although there is not perfect negative correlation we can still say that some sort of negative correlation is occurring, meaning that mileage negatively influences price. The relationship between mileage and selling price is inversely proportional; as the mileage of the car increases the selling price decreases, and as the mileage of the car decreases its selling price will increase. This is because a higher mileage means that the car has been used a lot, and so the car will tend not to last as long as a car with a lower mileage.

On the graph you can see a line of best fit has been drawn, disregarding the outliers. The gradient of this line will tell us by how much the price falls for each mile travelled.

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Gradient =   y

                x

           =         £1500 - £6000         s=   -£4500     s= -£0.0642 / mile

              75000miles – 5000miles    70000miles

This means that on average, for every 10,000 miles travelled the car’s value depreciates by £642.86.

               

There is no real correlation that is visible here, emphasised by the fact that there are various prices for the same engine size, for a few different engine sizes. From this it is suggested that engine size does not affect ...

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