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  • Level: GCSE
  • Subject: Maths
  • Word count: 5138

Mathematics course work

Extracts from this document...


Mathematics coursework on used cars prices

Mathematics course work

Used car prices


In  this  investigation  I  will  see  what  affects  the  prices  of  a  second  hand  car. I   will  analyse  each  category  with  tally  and  bar  charts. For  this  investigation  I  will  pick  out  30  cars  from  the  Internet. From  these  30  cars  I  will  see  which  cars  affect the  price  of  the  second  hand  car.

These are the cars I chose from the Internet.

10 BMW cars.        10 Audi cars                     10 Mercedes cars

BMW 316i        Audi A3                           Mercedes CLK

BMW 318i        Audi S3                            Mercedes SLK

BMW 320i        Audi A4                           Mercedes E-class

BMW 325i        Audi S4                            Mercedes S-class

BMW 330        Audi RS4                         Mercedes C-class

BMW 520i        Audi RS6                         Mercedes SL 55

BMW 730i        Audi S8                            Mercedes CL 55

BMW M3        Audi TT                    Mercedes A-class

BMW M5                    Audi S2                            Mercedes SL 500

BMW 850i        Audi RS2                         Mercedes CL 500

My task was to find out what influences the price of a second hand car.

To compare any data from these cars, I must at least pick out 5 models of cars then analyse it. The data that I will use is from the Internet. I will take each category and investigate the reasons that affect the price of a second hand car when it was new.

The first category I will look at is for the Age.

My hypothesis for this category is that the lower the age a car has then the higher price the car will be.

Here is a table that shows 5 BMW cars.




Price when new

Second hand price


























With the information in the table above, I will draw a stem and leaf diagram so that it is easier for me to find out the mean, mode and median.

I have listed the ages of the cars in order of size.

2, 4, 7, 9, 10,










Key: 1     0     this means the age of 10

...read more.


With the interquartile range I can find out the semi-interquartile range.

To do this I have to divide the interquartile range by 2.

5 / 2 = 2.5                  the semi-interquartile ranges of the 5 cars is 2.5.

The Audi car with the highest age is the Audi A3 with the age of 12. The Audi with the lowest age is the Audi RS6 with the age of 2. From these 5 cars the car that has the lower age will cost more then the car with the highest age, my hypothesis was right. The car price when it was new doesn’t only change because of its age but other things that come fixed with the car like the fuel, engine size, and seats.

Sometimes the colour, style and the gears can make changes to the price as well. The Audi RS6 is a much higher class then the Audi A3. This could also change the car price.

Now I will show a line graph to show the trends of the 5 cars.


By looking at the line graph I can say that again it has a weak negative correlation because when the age is low (2) the price is high (£20000) and when the age is high (12) the price is low (£3500) so the conclusion for this is that the lower the age the higher the price of the car and the higher the age the lower the price will be.

The graph matches my hypothesis, which I was right.

To find out how much price is reduced every year, I will have to find out the differences of the car prices. To do these I will subtract the new price with the second hand price.

I will use the last Audi car in the table, which is the RS6.

60000 – 20000 = 40000

The difference of the Audi RS6 is £40000.

...read more.


I have proved above by showing tables and graphs of 5 BMW and Audi cars that the higher the mileage a car has then the less the car will cost and the lower the mileage the more the car will cost. But in some cases the mileage will be higher then another car like the Audi RS6 has a higher mileage then the Audi S3 but the Audi RS6 still costs more then the S3.

Overall I think that the higher the mileage the lower the car price and the lower the mileage the higher the car price will be.


In this coursework my task was to see what influences the price of a new car to the second hand car price. I chose three categories and investigated them to see what happens. In the first category I looked at the ages of different cars an saw that the higher the age of a car, then the less the car price would be later on I found out that I can use the differences of a car and see how much is reduced every year.

The next category I investigated was the colours of the car. I investigated if the colours of the car decreased the car price, which in some cases did, but in other cases it didn’t. For this category my hypothesis was ‘the rare coloured cars have a higher price as the un-rare coloured cars will cost less’. By showing tables and graphs my hypothesis was correct.

The last category I investigated was the car mileages of 5 BMW and Audi cars. I found out that if a car has a high mileage then the car will be cheaper then a car that has a low mileage but in some cases it didn’t as I have shown in the Audi car mileages.

Overall I think that the investigation was successful and also interesting on finding what type of categories that influences the car prices.


...read more.

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