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Mathematics coursework on used cars prices

Mathematics course work

Used car prices

Introduction

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.

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

The mean age of these 5 BMW’s is:

2 + 4 + 7 + 10 + 11 = 34

34 / 5 = 6.8 or 7

The mean age for these 5 BMW’s is 7.

There are no model values for these cars because there are no common ages but there is a median age. In order to find the median I will have to put the age in order of size.

2 4 7 10 11

The median age for the 5 cars is 7.

To find the range of these cars, I will have to subtract the highest age with the lowest age.

11 – 2 = 9

The range of the 5 cars is 9.

To go in further more I can find out the Interquartile range of the 5 cars.

Again I have to put the age of the cars in order of size.

 

To find the interquartile range I must find the lower and upper quartile.

In this case they are:

 

Lower quartile

2 4 7 10 11

Upper quartile

2 4 7 10 11

The lower quartile is 4 and the upper quartile is 10.

Now I have to subtract the lower quartile with the upper quartile to find the inter quartile range.

10 – 4 = 6               the interquartile range of the 5 cars is 6.

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

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

6 / 2 = 3                  the semi-interquartile ranges of the 5 cars is3.

The BMW with the highest age is the BMW 316i with the age of 11. The BMW with the lowest age is the BMW 330i with the age of 2. From these 5 cars the car that have 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.

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 it has a weak negative correlation because when the age is low (2) the price is high (£10995) and when the age is high (11) the price is low (£3995) 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 of the car.

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 first BMW, which is the 316i.

15995 – 3995 = 12000

The difference of the BMW 316i is £12000.

With the difference I will divide it with the age of that car.

12000 / 11 = 1090.9091

1090.9091 this is how much is reduced in one year.

So the BMW 316i has an age of 11 and in one year 1090.90991 was reduced so after 11 years:

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1090.9091 X 11 = 12000.

£1090.9091 was reduced which matches the difference between the price when it was new and the price when second hand, with this I can find out how much will be reduced in: 2,3,4,5,6,7,8,9, years an so on by just multiplying by the number of years I want it to reduced.

In two year this is how much is reduced: £1090.9091 X 2 = 2181.8182

In three yeas this is how much is reduced: 1090.9091 X 3 = 3272.7273

I cannot predict how much the price will be reduced in the ...

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