# I predict that all the cars that I have chosen at random will have similar attributes, but in detail they will be completely different and therefore not comparable.

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Introduction

Xavier H Keenan 148

Stowe School

Maths Coursework

Mathematics Statistics Coursework

Winter 2002 - Used Car Prices

Introduction:

I am going to investigate what influences prices of second hand cars, and look into how car prices depreciate and what causes this. I am examining 55 randomly chosen cars taken from the supplied list and from ‘Auto Trader’ magazine, which I supplied. I am going to examine the relationship in the sample between the age, mileage and price. I am going to narrow down the in 3 stages from all cars to only 1998 Ford Fiestas. From this, I will draw the conclusions from the examination about how the price decreases and what affects this.

Section 1 – Random Cars

Hypothesis 1:

I predict that all the cars that I have chosen at random will have similar attributes, but in detail they will be completely different and therefore not comparable. I predict:

- The older a car is, the more miles it would have been driven.
- The more miles it has been driven, the less it costs.
- As the vehicle ages, it will be worth less.

Data Collection 1:

I have chosen to use the make and model of each car, because that is vital to know what car is being bought/sold or examined. I also chose the year it was first registered, because I want to prove that the older a car is, the more miles it will have been driven. So the mileage is important too. Little things could be used too, but I think that it is not worth including every little detail, and so I did not choose the minor things, like air conditioning, central locking, colour, electric windows… etc. These minor characteristics will all affect the final second hand price of a used car, but the make, model, mileage and year are the main determinants.

Middle

Data Representation 2:

Scatter Graph 4 - Price against Mileage

If you look at the graph, you can see that there is a medium strong negative correlation. We can see that as the mileage decreases, the prices declines with it. It has one anomaly, which is the ‘Mondeo Ghia’. It still agrees with my hypothesis that the older a car is, the more miles it has been driven. These results are quite scattered and they are quite poor results.

Scatter Graph 5 – Price against Year

If you look at the graph, you can see that there is a medium strong positive correlation. We can see that as the year decreases, the price declines with it i.e. the older the car, the cheaper it gets. It is still a little anomalous, with the largest as the ‘Mondeo Ghia’ and another anomaly being the ‘Sierra Sapphire’. This graph also agrees with my earlier prediction that as the car ages the less money it costs.

Scatter Graph 6 – Mileage against Year

If you look at the graph, you can see that there is a very strong negative correlation. We can see that as the year decreases, the mileage increases with it i.e. the older the car, the more miles it has been driven. There are no anomalies, but the overall results are not very tight they are very spread. This graph also agrees with my hypothesis, that as the as the car ages, the more miles it has been driven.

Pie Chart 2 – Ford Models

If you look at the pie chart, it shows the model of Fords in proportion of the 30 Fords in my sample. In order to get the best accuracy from the sample, I will choose the model of Fords with the largest representation. We can see that Ford Fiestas are the most popular with 40%.

Conclusion

We can see this effect, on graph 2 in section 1. Where the deviation above the line of best fit is greater than the deviation below the line.

Overall Conclusion and Summary:

- From all of my data, I can conclude that cars taken at random cannot be statistically compared, because the variations caused by the make, model, mileage, and date of first registration are generally too great.
- As a vehicle gets older, the price decreases with inverse proportion. The biggest decrease in age is when it’s nearly new, but the rate of price decrease gets less as the car ages. (See graph 8a)
- For cars of the same year, the more miles a car has been driven, the lower its price becomes (See graph 10)
- As the sample of cars becomes more selective, we can see that all the results then become more accurate and tighter to the best-fit line.
- Using mainly the cumulative frequency graphs (and graph 2), I can conclude that from the latter results, that the cars above average price have a wider range of prices than cars of below the average price.

Limitations:

- The main reason I only used 20 Ford Fiestas from 1998 was because there was only 21 Ford Fiestas in the ‘Auto Trader’ magazine.
- My sample size was quite small, because
- I didn’t look at the condition of the car (e.g. if a builder used it to carry bricks, or if it was for weddings, the condition would be quite different!)
- I didn’t take into account the extra’s that could affect the final price of the car, like air conditioning, colour, central locking…etc
- Some scatter graphs have best fit lines as curves, but I only showed this on one (8a)
- The sample size becomes smaller and therefore less reliable, as the types of cars gets narrowed down

This student written piece of work is one of many that can be found in our GCSE Gary's (and other) Car Sales section.

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