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# To find out if the mileage that a car has run is related in any way to the percentage decrease in the price of the car from original price to secondhand price.

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Introduction

GCSE Math practice coursework

The percentage decrease in price and mileage

Aim

To find out if the mileage that a car has run is related in any way to the percentage decrease in the price of the car from original price to secondhand price.

This would be worthwhile doing as the mileage directly affects the quality of the car and so, affects the price.

I will do a pretest (graph of everything) to ensure that the investigation is worth doing, just to see if there is an overall correlation.

Method

I will pick out the data I need for this project and take samples. Here I will need the statistics of mileage and both prices then use the spread sheet to work out the price decrease percentage.

Middle

∑ x;y - ∑x; ∑y               ∑ x2 – (∑x;)2                                  ∑y;2 - (∑y;) 2

n        n                               n

Prediction

I think that there will be a strong positive correlation as usually, the price drops by a greater percentage as the mileage increases.

Hypothesis

I think that this will be true as older cars get sold for less money. This is generally what happens but in some circumstances, for example, a 7 year old Rolls Royce  that has traveled 100000 miles can cost more that a brand new Toyota.

Results

The pretest graph:

This showed that the data has strong positive correlation and would be worth investigating into.

Conclusion

Here are the correlation coefficients for all my three samples:

Sample 1:  0.989297        Sample 2: 0.989546        Sample 3 : 0.990238

All the scatter diagrams show a strong positive correlation as their points nearly make a straight line.

Conclusion

From the results, I have made the following observations:

Using a scatter diagram, I found that there is a strong positive correlation between the percentage decrease and mileage

·With either of X or Y, I could estimate the other with the line of best fit.

The cumulative frequency tells me that most cars decrease between 20 and 40 percent in price.

Evaluation

The investigation could have been brought to a greater extent if more strategies have been used to analyze the data such as box and whiskers diagrams or histograms at the start of the coursework.

The observations were as predicted and the results were acceptable.

This student written piece of work is one of many that can be found in our AS and A Level Probability & Statistics section.

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