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. I also don’t know the condition of the vehicles, which will also make an impact on the final price of the car. I also believe this to be a secondary factor.

## Method of Data Collection 1:

To collect the raw data for my 55 cars, I used a stratified random sample. I had two main sources to collect my data; my own personal ‘Auto Trader’ car magazine, and the 100 random used cars and their attributes given to me from the teacher. I used 23 vehicles from the magazine, and 22 from the given data. To work out which cars I was going to select, I used the random number generator on my calculator, by pressing 2ndF, 7, =. This produced fifty-five random three-digit numbers. Because the Auto Trader does not reach one thousand pages, I would only use the last two digits, unless it was 199 or under. This was for the reason that it only has 199 pages! I would then only use the last two digits for my 22 cars of 100 sample cars given to me. Having the page numbers of the magazine, I simply took the first car from each of the pages, and the number of the car from the prearranged sample.

Justification of Method of Data Collection 1:

I used a stratified random sample method to make sure that I got data that would satisfy a fair test of randomness, and so I had a varied, non-biased sample of cars. To have the price as the dependent variable, I must change one thing at any one time, and keep the rest constant. I chose to investigate 55 cars because with this large amount of data, if I find a trend I will be able to say that it is reliable and therefore the statistical sample is large. I used my calculator to produce random numbers because this is a way that I can be sure that I will get random numbers.

Data Representation 1:

## Scatter Graph 1 – Price against Mileage

If you look at the graph, you can see that there is a weak negative correlation. We can see that as the mileage increases, the price declines with it. There is one anomaly, which is the ‘Bentley Turbo R’. This 1st graph agrees with my prediction, because I thought that the older a car gets, the more miles it has been driven. We can see, that the results below my line are more compact, rather than above they are more spread out.

Scatter Graph 2 – Price against Year

If you look at the second graph, you can see quite clearly that there is a weak 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. There are two major anomalies, which are the ‘Bentley Turbo R’ and the ‘Rolls Royce Silver Spirit’. This graph also agrees with my hypothesis, I stated before that the older a car gets, the less it costs. These results are quite close together, and we still have the pattern that there are more spread results above rather than below the line.

Scatter Graph 3 – Mileage against Year

If you look at the graph, you can see that there is quite a 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 all the results are very spread out around the line. This third graph agrees with my earlier prediction too, because I predicted that the older a car is, the more miles it has been driven.

Pie Chart 1 – Make of Cars

If you look at the pie chart, it shows the make of cars in proportion of the 55 vehicles in my sample. In order to get the best accuracy from the sample, I will choose the make of car with the largest representation. We can see that Fords are the most popular with 26%.

Justification of Data Representation 1: