The Percentage Decrase in Price of a Car and Its Mileage


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The Percentage Decrase in Price of a Car and Its 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.

I will test them for any relation they may have and draw scatter
diagrams.

The scatter diagrams would have lines of best fit.

A cumulative frequency table may also be useful in finding the
relations.

l Data

The information I need to collect are the prices and the mileage.
These are available in the excel spreadsheet from the KGV math site
and I will be working form this. The spread sheet is reliable as it is
provided for us. It contains a sample of 100 cars.

I will take three samples of 10 using stratified sampling (taking a
few from each 10) and leaving out the extremes from both ends. This
will give a fair sample as all the different percentages are taken
into account.

The samples will be compared to each other to find if there is a
correlation.

I will also find the correlation coefficient using the formulas:

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

[IMAGE][IMAGE][IMAGE] 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.

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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:

[IMAGE]

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

The correlation coefficient of the original sample was: 0.9865 this
figure is very close to 1.00 and so, this also proves that the sample
has a very strong positive correlation.

The cumulative frequency table allows me to work out the divination by
the formula:

n∑x2 -(∑x)2 = 38.71366

n2

The cumulative frequency curve shows that most cars have dropped
between 20 and 40 percent from their original price and at that point,
their mileage would have been from 24000 t o 50000.

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.


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