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 ages above 11 because then the price that will be reduced will be higher then the normal price.
Hence, if the car was more expensive then £15,995 then price that are going to be reduced can be reduced in the number of years you want it.
My prediction is right as the higher a age a car has the less the price will be and the lower the age a car has then the higher the car price will be.
To see if my above statements are correct, I will use another 5 Audi cars. I will do exactly the same as I did for the BMW cars.
Again I will use the same hypothesis for this category that is the lower the age a car has then the higher price the car will be.
Here is a table that shows 5 Audi 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 the mean, mode and median.
I have listed the ages of the cars in order of size.
2, 6, 8, 11, 12
Key: 1 2 this means the age of 12
The mean age of these 5 Audi’s is:
2+6+8+11+12=39
39 / 5 = 7.8 or 8
The mean age for these 5 Audi’s is 8.
There are no model values for these cars as well 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 6 8 11 12
The median age for the 5 cars is 8.
To find the range of these cars, I will have to subtract the highest age with the lowest age.
12 – 2 = 10
The range of the 5 cars is 10.
Again I can find out the Interquartile range of the 5 Audi cars.
First 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 6 8 11 12
Upper quartile
2 6 8 11 12
The lower quartile is 6 and the upper quartile is 11.
Now I have to subtract the lower quartile with the upper quartile to find the inter quartile range.
11 – 6 = 5 the interquartile range of the 5 Audi cars is 5.
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.
With the difference I will divide it with the age of that car to see how much is reduced in one year.
40000 / 12 = 3,333.3333
3,333.3333 this is how much is reduced in one year.
So the Audi RS6 has an age of 12 and in one year 3,333.3333 was reduced so after 12 years:
3,333.3333 X 12 = 40000.
£3,333.3333 was reduced in one year 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 and so on by just multiplying by the number of years I want it to reduced.
In two years this is how much is reduced: £3,333.3333 X 2 = £6,666.6666
In three years this is how much is reduced: £3,333.3333 X 3 = £9,999.9999
I predict that in 10 years this is how much is reduced: £3333.3333 X 10 = £30,000
Hence, if the car was more expensive then £60,000 then £30,000 could be reduced in 10 years.
My prediction is once again right.
My conclusion for the category Age
I have proved above by showing tables and graphs of BMW and Audi cars that the less the age a car has then the more the car will cost and the more the age a car has then the less the car will be.
The next category I will investigate is the colour of 5 Mercedes cars, 5 BMW cars and 5 Audi cars. I will see if the colour of a car influences the price of a new priced car when it becomes second hand.
My hypothesis for this category is that the rare coloured cars will cost more then the un-rare coloured cars.
First I will look at 5 Mercedes cars.
With only the colours of the cars I cannot find the averages but I can find the mode colour, which is Red because that is the colour that come up most out of the 5 cars.
I will see if the colours of these cars affect the car price. From the table above I can see that the coloured car that cost more is the colour gold. I think the price of the gold car is expensive because gold is a rare colour to find in a car. As you can see above all three red colour cars are less expensive then the other coloured cars.
Not many car buyers look at the colours of a car but look mainly at other things like the mileage, service history, age etc. I think the colour does affect the price of a second hand car because in the table above I can see that the Mercedes Clk cost £18000 when it is second hand and the Mercedes Slk costs £16000 when it is second hand. From my knowledge of cars I know that a Mercedes clk is a more high-class car then the Mercedes slk as the colours of the cars prove that a less rare coloured car costs less then a rare coloured car.
Now I will show a table for the colour of the cars above.
This is a bar chart that shows the colours of the Mercedes cars. As you can see the gold colour car has the highest second hand car because the Mercedes Clk has the colour gold which is a rare colour to get in a car. The two red colour cars have the least second hand price because red is not a rare coloured car.
As you can see the Mercedes Clk also is a red colour car but has a high second hand price because the car it self is a much higher class car then the Mercedes e-class c-class and the s-class.
Now I will investigate the colours of 5 BMW cars and also see if the price is affected when it is second. I will also see if a rare coloured car has a higher second hand price then a normal coloured car.
I predict that the rare coloured cars like gold, burgundy, or other unknown coloured car will have a much higher second hand price then a normal coloured cars like red, blue, green etc.
Once again I can’t find the averages of these colours but I still can find the mode colour. The modal colour of these 5 BMWs is the colour blue. This is because the colour blue appears the most in the table.
I will see if the colours of these cars affect the car price. From the table above I can see that the coloured car that cost more is the colours gold and Burgundy. I think the price of the gold and burgundy cars is expensive because these are is a rare coloured to find in a car. As you can see above the two blue colour cars are less expensive then the rare coloured cars.
As you can see the same thing is happening as the rare coloured cars did cost more then the normal coloured cars. In the table the BMW 316i has the colour of blue and the BMW 330i also has the colour of blue but the 330i costs more then the 316i. This is because the BMW 330i is a much higher class BMW then the BMW 316i.
From the table above I can say that the BMW 316i has a less second hand price then the other BMW car, which is also blue, because the BMW M3 is a much better rank car then the BMW 316i. It is only because the car is better but it is also because the M3 has a less age then the BMW 316i.
As can see that the gold colour car costs the most not only because of its model and age but because it has a rare colour which also makes the car a higher second hand price.
Once again my prediction was right as I said that the car that ahs a rare coloured car has a higher second hand price as in the table above the rare coloured cars are the BMW 330i and the BMW M5.
Now I will choose five Audi cars to investigate their colours and see if it influences the price of the cars.
First I will look at 5 Audi cars.
With the colours of these cars I cannot find the averages but I can find the mode colour, which is White because that is the colour that come up most out of the 5 cars.
I will see if the colours of these cars affect the car price. From the table above I can see that the coloured car that cost more is the colour Burgundy. I think the price of the Burgundy car is expensive because this is a rare colour to find in a car. As you can see above the two White colour cars are less expensive then the other coloured cars.
Now I will show a bar chart of the 5 Audi car colours.
Again I can say that the 2 Audi cars that are white are the 2 cars that have a less second hand price then the other Audi cars because white is another colour that is not rare to find in a car. The rare colours in these five cars are the Audi RS2 and the Audi TT. As you can see above in the table the two cars have rare colours which are burgundy and night fire. These cars have the highest second hand price out of the five cars shown in the table.
Again the rare colour car costs the more then the un-rare colour cars not only because of its model and age but also because of its rare colour which makes the car a higher second hand price.
Once again my prediction was right as I said that the car that ahs a rare coloured car has a higher second hand price as in the table above the rare coloured cars are the Audi TT and the Audi RS2.
In reality I don’t think the price of a car that is second hand is affected by the colour that much because when a car that has been published, it comes with a colour that you cannot change. When the same car becomes second hand the colour will still be the same colour, as it wouldn’t change unless someone re-sprays the car. The price of the colour can change if the car colour has a lot of scratches or has a cheap re-spraying job.
My conclusion for the category colour.
I have proved above by showing tables and graphs of the 5 BMW and Audi cars that the rare coloured cars like Gold, Burgundy, silver, night fire have a higher second hand price as the un-rare coloured cars like red, blue, white, silver have a less second hand price. My hypothesis that I have set at the beginning of the category ‘colour’ was right. Overall I think that the colour of a car does change the price of the car but not by a large amount.
The next category I will investigate is the mileage of the three types of cars.
I will choose at least five cars to see if the mileage of a car influences the price of a new car.
My hypothesis for the car mileages is that the higher the mileage a car has then the less the car will cost.
Now I will show a table of five BMW cars with its new and 2nd hand price and the mileage of each car.
With the information that I have found above, I will now draw a stem and leaf so that it is easier for me to find out the mean, mode and median.
The common stems are 2000 and 0000.
To find out the median stem, I will have to put the mileage in order of size. (Small to big)
0000, 0000, 2000, 2000, 4000
So the median mileage is 2000
To find the median leaf I will do the same.
2, 3, 8, 14, 16
The median leaf is 6.
In the table I have found out that there is a frequency of one each.
Now I will find the mean mileage size. To do this I will add the five mileages together and divide by the number of mileages I am investigating. In this case there are a five.
22,000 + 32,000 + 84,000 + 140,000 + 160,000 = 438,000
438000 / 5 = 87,600
The mean mileage size of a BMW car is 87,600
There are no modal mileages in this table as there isn’t enough information. To find the modal mileage there will need to be at least 2 or 3 mileages which are the same amount. In this case there isn’t.
To find the range of the mileage I will have to take away the highest mileage from the lowest mileage.
160000 – 22000 = 138000
The range mileage size of a BMW car is 138000.
With this information above I can find the interquartile range of the mileages. First I have to put them in order of size.
22000, 32000, 84000, 140000, 160000
To find the interquartile range I must find the lower and upper quartile range.
22000, 32000, 84000, 140000, 160000
The lower quartile is 140000 and the upper quartile is 32000.
To find the interquartile range I must subtract the upper quartile with the lower quartile.
140000 – 32000 = 108000
The interquartile range is 108000. Now I can also find the semi-interquartile range by dividing the interquartile range by 2.
108000 – 2 = 54000
The semi-interquartile range is 54000.
Now I will show a scatter graph of the car mileages.
In the scatter graph it shows the mileages of the five cars. When the mileage is high (160,000), the price is low (7995) and when the mileage is low (22,000) the price number is high (10000). This proves that if the mileage on a car is high the cheaper the car will cost and if the mileage is low the expensive the car will be.
The BMW car with the highest mileage is the BMW 730i with the mileage of 160000. The BMW car with the least mileage is the BMW 320i with the mileage of 22000. With the two mileages I can say that the BMW 730i has a lower second hand price then the BMW 320i. The second hand price of the BMW 730i is £7995 and the second hand price for the BMW 320i is £9000.
From the table above the BMW 730i costs more then the BMW 3220i when it was brand that is because the 730i is a much higher model then the 320i. By looking at the two mileages of the cars I can now say that my hypothesis was right, as I have shown above that a new car that costs more then another new car has a less second hand price then the other car.
I will choose another five cars to see if the mileage of a car influences the price of a new car.
I will use the same hypothesis for the Audi cars, which is the higher the mileage the cheaper the car will cost.
Now I will show a table of five Audi cars with its new and 2nd hand price and the mileage of each car.
With the information that I have found above, I will now draw a stem and leaf diagram so that it is easier for me to find out the mean, mode and median.
The common stems are 1000 and 000.
To find out the median stem, I will have to put the mileage in order of size. (Small to big)
000, 000, 0000, 1000, 1000
So the median mileage is 0000
To find the median leaf I will do the same.
12, 3, 5, 5, 18
The median leaf is 5.
In the table I have found out that there is a frequency of one each.
Now I will find the mean mileage size. To do this I will add the five mileages together and divide by the number of mileages I am investigating. In this case there are a five.
12,000 + 31,000 + 51,000 + 50,000 + 180,000 = 324,000
324000 / 5 = 64,800
The mean mileage size of a Audi car is 64,800
There are no modal mileages in this table as there isn’t enough information.
To find the modal mileage there will need to be at least 2 or 3 mileages which are the same amount. In this case there isn’t.
To find the range of the mileage I will have to take away the highest mileage from the lowest mileage.
180000 – 12000 = 168000
The range mileage size of an Audi car is 168000.
With this information above I can find the interquartile range of the mileages. First I have to put them in order of size.
12000, 31000, 50000, 510000, 180000
To find the interquartile range I must find the lower and upper quartile range.
12000, 31000, 50000, 51000, 180000
The lower quartile is 51000 and the upper quartile is 31000.
To find the interquartile range I must subtract the upper quartile with the lower quartile.
31000 – 51000 = 20000
The interquartile range is 20000. Now I can also find the semi-interquartile range by dividing the interquartile range by 2.
20000 – 2 = 10000
The semi-interquartile range is 10000.
Now I will show a scatter graph of the car mileages.
In the scatter graph it shows the mileages of the five Audi cars. When the mileage is high (180,000), the price is low (4500) and when the mileage is low (12,000) the price number is high (20000). This proves that if the mileage on a car is high the cheaper the car will cost and if the mileage is low the expensive the car will be.
From the scatter graph above I can say that even though the Audi RS6 has a much higher mileage then the S3 but the RS6 will still cost more then the S3 because the RS6 is a much higher class car then the S3.
Conclusion for the car mileages.
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.
Evaluation
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.
