CUMULATIVE FREQUENCY:
Ages is found like this; (C.F Is the Cumulative Frequency)
From this graph we can tell that the age’s median and lower quartile and upper quartiles: the median is 100 / 2 = 50, so it’s the 50th position, which form the table above you can tell that the 50th position lies in the 6th year, just 3 numbers off from the 5th year, which is why on the above graph, it looks like 5th year. The range is 15 – 1 = 14. From the above chart, I will create a box plot, which will help to show my results more clearly, and tell me if its positively or negatively skewed
The lower quartile is 100 / 4= 25
The upper quartile is 100 / 4 = 25 X 3 = 75
SAMPLING:
30 CARS:
I have chosen 30 cars by using the random button on my calculator, so I can work out what factors affect the price of a second hand car.
The following numbers came up on the calculator:
The following cars were chosen (can be seen above):
LOSS OF VALUE:
For each car in my sample, I need to work out the depreciation of it. This is found out by, the following formula:
Original value – New value = difference in value
Difference in value X 100 = percentage of depreciation
Original value
For example: for the first car, which’s data has been given below:
Car no make model price (new) _ price (second hand).
1 Ford Orion 16000 7999
So the value is found out like this:
From the following table, you can see the depreciation values for all 30 cars:
Depreciation ranges:
AGE FACTOR:
From this graph you can tell that as the age of a car increases, so does its depreciation. Using the line of best fit; form this graph we can calculate how much a certain car depreciates at a certain age. For example a car that is 5 years old, will depreciate roughly to 70 % of its original value.
However this graph does have one car missing, which was the Volkswagen Golf, which didn’t have the price when brand new, so as a result I couldn’t work out the depreciation rate of it, causing it to be left out. However it wouldn’t have really affected my graphs trends, as they are quite obvious. However using the line of best fit I can work out, how much it would have roughly have depreciated to; as it was 15 years old, it would have gone down to % of its value. It also has a positive correlation. The axis starts from 20, as there are no cars that have a depreciation value of below 1, this tells me that in one year (the minimum age), a car depreciates at least 20%.
The equation of the line of best fit is :
From this graph above, we can tell that as the age of a car increases, the price of it decreases. There is also one anomalous result, reasons for which I will explain later on, in my conclusion. This graph also tells us whether there us an positive or negative correlation, in this case an negative correlation. In this graph there were no cars values missing, so all the data points have been entered. With this graph you can work out the rough price of a car, at a certain age. For example, a car that is 3 years old will be roughly £6500.
The equation of the line of best fit is :
MILEAGE FACTOR:
From this graph you can tell that as the mileage of a car increases, the depreciation value of it also increases. The line of best fit for this graph helps me to estimate the depreciation when the mileage of a car is given. For example a car that has 9000 miles will have depreciated roughly %.
However there are two cars missing from this graph as there were no recorded mileage for them, and as my cars were chosen randomly this is beyond my control. However using their depreciation value, which I have worked out previously, I, can work out what their rough mileage might be:
The first car is the Volkswagen golf, but unfortunately this car does not have a price when new, so I do not have a depreciation value. The second car can however be calculated, its Lexus LS400 and its depreciation is 84%, so we go across the y axis till we get to 84% and go across till we meet the line of best fit, and then go down, and that should tell us the mileage which is around 50, 000.
The equation for the line of best fit is:
ENGINE SIZE:
From this graph you can tell that the engine size doesn’t effect the depreciation of a car.
This graph doesn’t show a trend or anything. Al l we can gather from this is that the engine size is usually between 1.0 and 2.0 mainly. If we use the line of best fit, we can gather that an engine size of 1.5 depreciates %.
This graph doesn’t show much of a trend, except that most of the values tend to lie between 1.0 and 2.0.
CONCLUSION:
Overall, my hypotheses were correct with the exception of one. The price of the car did decreases as the mileage went up and as the age went up. However it was also incorrect, as the engine size has no effect on the price of a second hand car at all, as in the graphs no type of relationship between the two could be distinguished at all. I discovered that by using scatter graphs, and other charts, which helped me discovery a trend.
However there were limitations for me in this investigation, that were beyond my control, for example, as I used random sampling, I didn’t have control over which cars were chosen, so as a result, one car that was chosen didn’t have a when brand new value, so I could work out its depreciation, and the two other cars did not have any mileage recorded, so I had to leave them out unfortunately.
If I could get the chance to re-do this whole investigation I would use stratified sampling to see if I would see if it changes my findings in this one, or if the results still stay the same overall.
I am now going to investigate and compare two makes of cars and one factor, which will be age, to help me investigate which of the two makes depreciates the quickest.
FURTHER INVESTIGATION:
Now I have chosen for age to the factor I am investigating. The car makes are going to be Vauxhall and Ford, as there are a large majority f them. There are 16 Fords and 13 Vauxhalls and their details are below:
FORD DETAILS:
VAUXHALL DETAILS:
I will now do a cumulative frequency for Vauxhall and Ford ages to represent my data.
The ages for Ford are:
so now I will put them in a table:
This cumulative frequency graph shows us the lower and upper quartiles for the age in Ford cars. From the graph above you can see that the lower quartile is roughly 3, and the median is 5, and that the upper quartile is 7.the range for this is 10 (11-1 = 10). Also we can tell from this, the graph steady’s out at ages 8 - 9, which could be due to no values falling between there. I will plot a box and whisker diagram, which can be seen below for this graph.
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FORDS: the average price for Ford cars overall was found by adding up all the values and divided them by the number of values.
1595 + 4295 + 4700 + 3495 + 3995 + 2995 + 2300 + 1050 + 3200 + 1664 + 1995 + 8800 + 7995 + 7999 + 8250 + 1495 = 65823 = 4113.9 = 4114
The median is 3200 (8th value)
The range is 8800 – 1050 = 7750
The average age for Fords is:
7 + 3 + 5 + 7 + 5 + 6 + 7 + 8 + 4 + 10 + 7 + 2 + 4 + 1 + 3 + 11 = 79 = 4.93 = 5 years
16
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Now I am going to do a cumulative frequency diagram for the Vauxhall ages. These are the ages for Vauxhalls,
I will put this in a table now:
From the above graph, you can see that overall the car prices rose slowly, steadying twice which could be due to no cars actually falling in between this numbers. The median is 13 + 1 = 14 / 2 = 7, so it’s the 7th position, which is about 5. The range for this data is 9, (10 – 2 = 8), the lower quartile is 3.25, and the upper quartile is 9.75. The inter-quartile range is 9.75 – 3.25 = 6.5. Below you can see a box plot for this cumulative frequency graph.
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VAUXHALLS: the average price for Vauxhall cars was found in the same way as above.
6595 + 2900 + 3191 + 6995 + 850 + 4995 + 4976 + 3495 + 1000 + 7499 + 7999 + 6499 + 4995 = 61989 = 4768.3 = 4768
13
The median is 4995. (The 7th value)
The range is 7999 - 850 =7149
The average age for Vauxhalls is:
4 + 6 + 6 + 6 + 10 + 2 + 4 + 6 + 10 + 4 + 2 + 4 + 5 = 69 = 5. 3 years which is 5 years
13
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Box plots:
From these box plots I can tell that
FURTHER INVESTIGATION:
Now I am going to look at just one make which I have chosen to be Vauxhall, and I will choose three models, which will be Astra , Corsa and Vectra. I will compare these to see which of this decrease the quickest.
The average depreciation price for Astra is the following:
- 14325 – 6595= 7730 / 14325 X 100= 54%
- 13740 – 2900 = 10840 / 13740 X 100=79%
- 9795 – 3191 = 6604 / 9795 X 100 = 67%
67 + 79 + 54 = 200 / 3 = 66.8 = 67%
The average depreciation price for Vectra is:
- 18580 – 7999 = 10581 / 18580 X 100 = 56.9 = 57%
- 18140 – 6499 = 11641 / 18140 X 100 = 64%
- 13435 – 4995 = 8440 / 13435 X 100 =62.8 = 63%
57 + 64 + 63 = 184 / 3 = 61.3 = 61%
The average Depreciation price for Corsa is:
- 8995 – 4995 = 4000 / 8995 X 100 = 44.5 = 45%
- 7840 – 4976 = 2864 / 7840 X 100 = 36.5 = 36%
- 7440 – 3495 = 3945 / 7440 X 100 = 53%
45 + 36 + 53 = 134 / 3 = 44.6% = 45%
So from this you can see that the Vauxhall Corsa depreciates the least amount with 45%, while the Vauxhall Astra depreciates the most with 67%.
From this you can tell that age is a major contributing factor that affects the price of a second hand car, as well as mileage.
