# Test which factors affect the price of a second hand car using a variety of different statistical techniques

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Introduction

GCSE MATHS STATISTICS COURSEWORK

SPECIFY THE PROBLEM AND PLAN

Introduction

I am going to test which factors affect the price of a second hand car using a variety of different statistical techniques. From what I discover using these techniques I will conclude which factors are the most important.

I will examine only cars within the reach of a normal family, i.e. not luxury cars. I will also exclude classic cars as these are unlikely to perform like normal second hand cars.

Using a given set of data on the prices paid for second hand cars, I chose ten of these factors and did a survey of the class’ parents to make initial assumptions of which factors they were most influenced by when buying a second hand car. The survey asked them to choose the 3 most important and 3 least important from a list of ten. Using the results of this data, shown on page … , I selected three hypotheses to test. I will test these using a given data set. If I need to take more samples to test the hypotheses more conclusively, I will obtain data from other sources.

The types of information in the column represent the factors which can easily be defined when buying a car, even though there may be other ones that affect a person buying a car, even if they cannot be measured.

Middle

If the data is skewed then I will make box plots for each age group. To do this I will need to calculate the lower quartile, median and upper quartile. I would expect the median not to move much in relation to the lower quartile.

Collect, Process and Represent Data

Hypothesis 1

The cars I have excluded are 13, 54, 56, 71, 72, 73 and 95 as they all have original prices of over £25000. I have also excluded number 29 because it does not have an original price. This is probably because the car is so old (15 years old – the oldest car) that the value for original price could not be found out. I have also not shown numbers 69, 74 and 79 on the graph as they do not fit my scale. I will examine them individually after the graph to see if they fit the pattern.

As can be seen from the graph there is a positive correlation, albeit quite a weak one and with several anomalies, mostly in cars which are particularly expensive. This could be because when people buy a nicer model of car they will want to buy it new rather than second hand. The three cars above the £20000 mark included on this graph are all Rovers. The peculiarity of these results could also be due to something about people who buy Rovers.

Conclusion

Therefore its equation is y = -6x + 64

The gradient of the first line is (y6–y5) ÷ (x6 – x5) = (16 – 21) ÷ (10.667 – 7.667)

= -5 ÷ 3

= -1.667

Its y- intercept is 34

Therefore its equation is y = -1.667x + 34

These equations can be used as follows to find the expected percentage of original price a second hand car can expect to get due to its age. Let a represent age.

0 < a ≤ 2 years | Expected % of Original Price = -12a + 75.5 |

2 < a ≤ 7 years | Expected % of Original Price = -6a + 64 |

a > 7 years | Expected % of Original Price = -1.667a + 34 |

If I want to negate the effect of age on car I can remove the depreciation it causes from my data. To do this I will divide the actual percentage of original price of the car by the expected percentage of original price of the car. This will then give me a value which shows how the car has lost value in relation to what I would expect. It also means I can analyse other factors without it being distorted by age.

Therefore to find the % of original price of a car discounting the effect of age I use this table. Let a represent age and o represent the actual percentage of original price.

0 < a ≤ 2 years | % of Original Price Discounting Age = o ÷(-12a + 75.5) |

2 < a ≤ 7 years | % of Original Price Discounting Age = o ÷ (-6a + 64) |

a > 7 years | % of Original Price Discounting Age = o ÷ (-1.667a + 34) |

I can use this formula to work out percentage of Original Price Discounting Age for all of the cars.

This student written piece of work is one of many that can be found in our GCSE Gary's (and other) Car Sales section.

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