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• Level: GCSE
• Subject: Maths
• Word count: 4738

# Maths Coursework: Car Prices and Specifications

Extracts from this document...

Introduction

Hee-Who Park        Used Cars Sales         04/02/01

11AM        Maths Coursework

Maths Coursework:

Aim:

The aim of my investigation in this maths coursework is to investigate the used car sales. I will need to investigate on these variables:

• The price of the cars
• The age of the cars
• The makes of the cars
• The cost when new of the cars
• The mileage of the cars
• The engine sizes of the cars

All the variables above are ratio variables (Numbers are used) except the makes of the cars, because that one is special and it’s called nominal variables.

I will first try to find out any links between the current price of the car and the other variables such as age, mileage, car engine size, and the make. After finding links, I will then attempt to progress the data in order to find out stronger links between variables and eventually I will try to find a general value or formula that can link them.  I will be drawing some graphs and then look for conclusions, which can help me to find a general formula.

Here is the results table, which was given in this coursework:

 Car Number Price (Pounds) Age (Years) Make (Brand) Original Price (Pounds) Mileage (Miles) Engine Size (Litres) 1 6970 3 Ford 11600 24000 1.6 2 3350 7 Peugeot 7100 85000 1.1 3 3995 6 Ford 13800 52000 2 4 5300 6 Vauxhall 16300 70000 2 5 6500 3 Fiat 8700 24000 1.2 6 1500 9 Vauxhall 8700 82000 1.6 7 995 9 Ford 8500 102000 1.8 8 3000 7 Vauxhall 10400 63000 1.7 9 7495 1 Vauxhall 9770 8000 1.4 10 850 10 Ford 7540 124000 1.6 11 5595 4 Ford 11000 41000 1.6 12 4995 3 Ford 9880 34000 1.4 13 5595 4 Ford 14000 55000 1.6 14 4995 4 Rover 11500 40000 1.4 15 2600 7 Rover 12000 82000 1.6 16 1000 10 Peugeot 6200 119000 1.1 17 750 11 Peugeot 5100 96000 1 18 1350 8 Ford 9140 108000 1.6 19 2950 8 Ford 17750 96000 2.9 20 3250 7 Vauxhall 9990 86000 1.6 21 5650 3 Vauxhall 11150 34000 1.6 22 4600 2 Rover 7300 17000 1.1 23 5400 1 Rover 7300 11000 1.1 24 4800 1 Rover 7300 26000 1.1 25 2700 5 Fiat 13000 51000 2 26 11000 1 Peugeot 13800 9000 1.8 27 2800 5 Fiat 6500 43000 1 28 8000 4 Rover 21000 142000 2.3 29 6495 2 Ford 8800 23000 1.3 30 4050 4 Ford 8400 48000 1.3 31 6300 2 Ford 10300 26000 1.3 32 4100 4 Vauxhall 8900 37000 1.3 33 6600 1 Vauxhall 8500 9000 1.3 34 7800 1 Peugeot 10500 13000 1.4 35 8700 3 Vauxhall 16000 42000 2 36 2000 7 Peugeot 8300 65000 1.4

Hypothesis:

I predict that all of the variables will affect the Price of the cars in anyway, because they all are very important. So I think the Age will affect the price most, because it is the most important variable of all and I think the Engine Size affects the least, however all the variables will affect it in some ways.

Graphs:

1.

Middle

This graph clearly shows us that there is no correlation here in this graph between the Engine Size and the Price. The trend shows us that the bigger the engine size, the higher the price. But the relationship is very weak. Although there are 2 cars with the same engine size, the price difference is very big.

From this graph, we can conclude that:

• The Engine Sizes has no links between the Prices of the cars.

5. Previously, I did a graph on the relationship between the price and the engine size and the correlation came out not very strong. So this time I am going to bring in the Original price instead with the Engine size to see whether these two variables will have some sort of relationships.

I was surprised to get this kind of result from these two variables. Previously we had tried the graph with the Price and the Engine Size and it did not come out very well because there was no correlation, but this graph shows a strong correlation. This means both of the variables are closely linked. The y-intercept for this graph should show a positive value, because the car without the engine must cost something, but the value comes out as negative, which means there’s an error. From this, the conclusion can be made which are

• The original price of a car is directly proportional to its engine size.
• For every increase of one litre of the car’s engine size, its price increases 7528 pounds in average.

6. I think there will be a quite a strong link between the Original Price and the Price (Current price), because the higher the original price is, the higher the car price would be if the other variables don’t play a part in this.

Conclusion

The brand Fiat is the cheapest from the rest of the brandsFiat car is quite cheap due to a lot of variation in the size of the engineRover and Vauxhall are technically more expensive than the other brandsFord have the most expensive cars when it is newFord tends to have the biggest engine size than the rest of the brandsAll Peugeot cars have the smallest engine size than the rest of the brands, and that is why it makes them the cheapest cars when it is newThe brands have quite a big impact on the model formulae, and therefore each model formula has to be made for each brands to make the predicted price as near as possible to the real present priceThe average formula for all the brands is: . This is true, since the gradient and the y-intercept were taken from the graph where the rate of depreciation was against the age. On this particular graph, it was not done with each brand and contained all the brands.
• The model formulae that is used to each of the brands are as follows:

Fiat:

Ford:

Peugeot:

Rover:

Vauxhall:

• Each specifically specified model for each brands are much more accurate than the model which is the average formula for all the brands. The average formula for all the brands has the error of around ±1000, where as the each brand’s formulae has ±500 pounds of error. So I could conclude that each brands’ model is much more accurate.
• So it is the best to use the model function formula for each brand to get the most accurate results. But the predicted price may come out slightly faulty, but it would still be much more accurate than using the universal formula for all of the brands.

-  -

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