Maths Coursework – Used Cars

There are many factors that can influence the price of a second hand car, such as; model, make, age, engine size, mileage etc. For this coursework I will be using the following three factors in order for me to investigate what effects the price of a second hand car:

- Age
- Mileage
- Engine size

My reasons for choosing these three factors are as following:

Age:

People are more likely to acquire a car, which is new than old because old cars are commonly not as popular as the new ones as they are more likely to break down. Also, the public (especially the younger generation), would prefer to buy a new car because they are much more fashionable to have.

Mileage:

The mileage will be an important factor affecting the price of a second hand car because a car with a high mileage means that it has been driven a lot and this means that it is more likely to break down. Also it means that high maintenance will be required for the car to stay working whereas a car with a low mileage wouldn’t entail as much maintenance.

Engine Size:

The engine size is also another factor, which will affect the price of the second hand car greatly. The reason is that the larger the engine means that the quicker the car will go and in today’s society, a fast car would be essential and appeal to a lot of people.

For this investigation, I have come up with the following hypothesis:

“The mileage affects the price of a second hand car more than the engine size and the age of the car”

I will use the data provided and my own knowledge to find out if my hypothesis is true or false and how it can be corrected, if needed.

I have been given a database of 100 cars to help me with this investigation however I will not use all the cars because 100 cars are too much to work with. Instead, I will use 40 cars because then it will be an easier amount of cars to work with and the investigation will remain fair. To choose which cars will be included in my sample of 40, I have arranged the cars in order of frequency:

As you can see out of the 100 cars, the majority are Ford, Vauxhall, Rover and Fiat. Thus, it would be logical to use those four in my investigation because if I use all of the cars and come out with a sample of 6 Fords, 3 Vauxhalls, 1 Landrover, 1 Mazda etc, this will then make my investigation unfair because all of the cars do not have the same value and some cars are more exclusive than others. Having the four main makes in my database allows me to come up with conclusion about the rest of the makes.

In order to choose my sample of 40 cars I need a fair choosing method. I can simply take ten of each car to make 40 but this will not fair because we have 10 Fiat cars and this means that all ten of the cars have to be chosen. There will be no selectiveness process involved, which means that the investigation is unjust. Therefore, to retain the fairness throughout the experiment, I will use stratified sampling as a fair method. This is because stratified sample takes into account the make of the cars and the frequency, and also keeps the investigation thoroughly fair.

Method of stratified sample:

The total of the four cars (Ford, Vauxhall, Rover and Fiat) adds up to 51

My sample size is 40

Ford: 16/51 * 40 = 12.54901961 = 13 cars

Vauxhall: 13/51 * 40 = 10.19607843 = 10 cars

Rover: 12/51 * 40 = 9.411764706 = 9 cars

Fiat: 10/51 * 40 = 7.843137255 = 8 cars

Using the stratified sampling method above, I have got the number of cars I will choose for my final sample of 40, which I will use in order to continue my investigation. I now need to randomly select the 40 cars from the four makes. To do this, I will label the cars with their frequency, e.g. I will label the fords 1 to 16, and then I will use the RAN# on my calculator, which will show me a random number. I will then multiply that’s number by the frequency of the car e.g. I will multiply the number by 16 for the fords. This will then give me a value and I will choose the car, which is represented by that value. I will proceed with this method for all four car makes. This will then provide me a sample of 40 cars chosen in a fair and just manner.