Objective; to investigate the relationship between used car price and age of car.

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30/6/03 Mathematics Coursework C+H/WK

Objective; to investigate the relationship between used car price and age of car.

Equipment; to do this task I will need the following equipment;

Ruler,

Pencil,

Pen,

Multimedia computer (to write up investigation in neat),

And plenty of A4 paper.

My Hypothesis;

Since all the cars from the given data base are MODERN cars, I predict that they ONLY decrease in value once they are bought. It would be different for really old CLASSICS as they can be so old that they actually increase in their value as they age. This is because;

. The demand of these cars rises as few are left available, from being scraped.

2. Since theses cars lack modern technology of galvanised metal, they suffer from rust, thus people selling them in mint condition spent thousands of pounds restoring the car to it's original condition, hence they want that money back when they come to sell it.

3. The cars are different from modern cars, and give the owner a high status through being so immensely unique.

Because all these cars in the database are all modern, the cars should, in my prediction decrease in value as they age and those that are guaranteed to become classics may depreciate slower in value than those that aren't. Also those of luxury and prestigious names like Mercedes, Bentley and Rolls-Royce, and those that have a high demand will loose their value more slowly then those that aren't, but just as a generalisation, no matter what car i choose, the older it is, the lesser it's value is against those that are younger. This means that in the graphs I produce there is a TREND in the cars correlation which must be NEGATIVE in order for my hypothesis to be true.

Sampling; (Planning)

My plan involves selecting 40 cars from the total of 100 cars by car in the list. To do this I used stratified sampling which involved taking a tally of all the cars arranging them in sections depending on their age, then as 40/100 is 0.4 I multiplied the frequencies for each age group by 0.4 and rounded it to the nearest integer where the total would add up to 40 cars. I decided to leave out the cars of ages 11+ since their was only a maximum of one car for each year ,hence when I multiplied by 0.4 and rounded to nearest integer I got 0. Also because there were no cars of ages 12,13 and 14 years this would leave a massive gap in between 11 and 15 years, leaving under sufficient data in the graph to be properly analysed and a proper, proved conclusion to be made. I also did this because if I just picked out cars randomly like every 3rd car in the list, it wouldn't prove to be a fair test, as if I did, I may have neglected cars of certain ages out, and/or got too many cars of the same age group. Therefore, again incorporating this data onto a graph would leave massive gaps and the points would be too sparse in between to analyse properly and make a conclusion to the objective that is guaranteed true- with clear evidence from data and positive backup from my predictions of prices on other real cars from the remaining database.

The stratified frequency table overpage informs you of the list of cars of 1-10 years old, and the amount of cars that I will pick out after multiplying by 0.4 and rounding to it's nearest integer, so altogether the total will add up to 40 and my graph will be adequate enough to be fair, hence my conclusion confirmed fully true, my hypothesis confirmed either true or perhaps untrue, all from fair evidence in my investigation procedures and results.

For each number of cars I have to pick out I will choose each 3rd car from the database of that certain age group an take note of it's name and obviously it's used price. After I have acquired all this relevant information I will find the mean value for each car age group hence another graph as well as the first one(with all 40 cars pitched on it)that gives the mean value for each year. This is easier to follow since there are only ten points in comparison to the previous 40, therefore clearer for me to back up my conclusion to the task at the end, hence being is a better reference to see whether or not there is a strong trend between the data, as every cars values are equally blended in to the graph, and all equally count with no car, whether it was out of the trend in the first graph or not, neglected from it.

Stratified Frequency table to show how may cars from each age group are to be picked

Age of car in years

Frequency

40% of cars available

No. of cars to be picked

0

4

4

2

9

3.6

4

3

8

3.2

3

4

2

4.8

5

5

8

3.2

3

6

8

7.2

7

7

4

5.6

6

8

0

4

4

9

5

2

2

0

3

.2

2

Total = 97 cars

Total = 40 cars

As you can clearly see that the bottom one should have been rounded to 1 but I instead brought it up to 2. This is because 1 car alone is unsatisfactory, considering that the mean amount of cars picked is 4 and that 1 car hasn't enough range or even any of range prices, thus I'd get a more accurate measurement of the prices of 10 year old cars if another was added, making my conclusion even stronger for evidence and backup. And in the second graph I'd also get a mean price for ten year old cars between the two I'd picked, whereas with one, the mean, median and mode are all the same, reducing the test being fair and accurate to unacceptable measures.

Then, for picking each car from the data base for each respective age group, I decided that stating the name and type of the car is actually necessary, despite the fact that I am looking at the relationship of car age to used value and not car name/make to used value. This is because of if in the case of weird occurrences where one or more cars are vastly out of the other car values'trend',or even if there happens to be no trend at all! This is because knowing what the car is, should make it easier to explain why it doesn't follow with the other cars data's correlation. Obviously, after all is settled in this part of the task the next thing I would do is to incorporate the data into a scatter diagram which should interpret whether in general the prices go up or down depending on the type and how much correlation(If any) the graph shows.
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On each side of the graph should be, the age of the car(Going across the x axis ) and the age of the car going up along the y axis. This should be enough information, and proof for me to write my conclusion to the objective, making proof of whether my hypothesis is correct, why and what the relationship is, hence fairly and honestly evaluating and the task.

Below is the list of named cars that I picked from the database for each age groupie and the value of it in pounds(£)

Age 1 ...

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