# Maths Coursework: Car Sales

Hee-Who Park        Used Cars Sales         04/02/01

11AM        Maths Coursework

Maths Coursework:

Aim:

The aim of my investigation in this maths coursework is to investigate the used car sales. I will need to investigate on these variables:

• The price of the cars
• The age of the cars
• The makes of the cars
• The cost when new of the cars
• The mileage of the cars
• The engine sizes of the cars

All the variables above are ratio variables (Numbers are used) except the makes of the cars, because that one is special and it’s called nominal variables.

I will first try to find out any links between the current price of the car and the other variables such as age, mileage, car engine size, and the make. After finding links, I will then attempt to progress the data in order to find out stronger links between variables and eventually I will try to find a general value or formula that can link them.  I will be drawing some graphs and then look for conclusions, which can help me to find a general formula.

Here is the results table, which was given in this coursework:

Hypothesis:

I predict that all of the variables will affect the Price of the cars in anyway, because they all are very important. So I think the Age will affect the price most, because it is the most important variable of all and I think the Engine Size affects the least, however all the variables will affect it in some ways.

Graphs:

1. First of all, I will be comparing the prices of all thirty-six cars with their age and the mileage. I believe in terms of the general knowledge as the age/mileage of the car increase, the price of the cars should become cheaper. For example, if a car has been driven a lot, it would surely have depreciated as it has been used a lot. Therefore the age and the mileage will definitely affect the price of cars.

As you can see on this graph above, as the car gets older, the price goes down. This also shows that a car that is new depreciates at a faster rate than a car that is older. This can be explained quite logically. If a car is 1 year old, it should drop at a higher rate per year where as a 20-year-old car that no one wants to buy should drop at a lower rate per year. So the price depreciates slower as the age goes up. Also, this graph is correct in showing that no matter how old the car is the price will not go to a negative value. If this were the case, the car sellers would give money to those who will buy the car, which does not happen.

And also if the graph was examined more carefully, another fact could have been revealed. The residue value is getting smaller as age increases. In other words, it shows that for a relatively new car, its price maybe hard to determine by its age. But for a rather old car, its price maybe fairly accurately estimated from its age. For example, the price of 2 cars which are one year old can vary between 11000 pounds to 4800 pounds, where as the price of cars which are both ten years old can vary from 850 pounds to 1000 pounds.

So from this graph, we can make a conclusion as the following:

• As the age of a car increases, the price also decreases.
• No matter how old the car is the price, it will never come out as a negative value.
• As the age of a car increases, it becomes more and more dominated variable for estimating its price.

2. The graph below is the Price against the Mileage to see whether it affects the price of the cars. I believe the mileage will affect the price, because as the car has been used up a lot, then certainly the price will go down.

This graph also shows the exact same thing as the first graph, because the price drops as the mileage increases. And also showing a negative correlation as the price drops faster when the car is younger than the older and the price will never reach a negative price. It might slow down less and less but will not reach a negative value. However, there’s a point in red on the graph where it is far out of place than the others. This is because its price is much higher than the other cars where it has been used more frequently than the others, because the mileage is very high. This special car has much higher price than the most of the cars, which have the similar mileages. This is because its age is relatively small. So this special car’s mileage is very high even though its age is very low, compared to the other cars.

From this graph, we can conclude the following:

• As the mileage of a car increases, its price decreases.
• As the mileage of a car increases, it becomes more and more dominated variable for estimating its price.
• For cars with small mileages, their prices vary very much by other variables, such as the brand or engine size. Where as for cars with low mileages, their prices largely depend on their mileages. Same situation as the one in the graph, relationships between the Price and the Age.

3. From these two graphs above, I can conclude that since ...