# Data Handling

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Introduction

MATHS

COURSEWORK

YEAR 11

11GRS

CAR’S COURSEWORK

Maths Coursework

2004

I will be investigating about what influence second hand car prices. This coursework is worth 21 marks and therefore I’m going to work hard in order to achieve the highest grade possible.

In this coursework I will be showing how factors such as mileage, age, engine size etc. affect the prices of second hand cars. I will be presenting graphs for all the factors that affect the prices and showing a comparison between the prices and each of the factors that I have stated.

PLAN

The aim of this investigation is to find out what influences the price of second hand cars. Second hand cars cost less than brand new cars due to factors such as mileage, Age, etc.

First, I will be deciding the key factors, which could influence second hand car prices and also the factors that have a low or zero affect on the prices of second hand cars. I will be deleting these factors from the database.

Here are the key factors.

- Age

- Engine size

- Mileage

- Insurance

- Number of Doors

- MPG

- Number of Owners

Here are the low affect factors.

- Style

- Central locking

- Seats

- Air conditioning

- Airbags

I have decided to use the first 48 cars on my database to gain an evaluation of what affects second hand car prices. I could not use all my database because the results will be vary also it will be very complicated, to understand and find out if the factor has any affection.

My next step is comparing. I will be comparing the key factors with price using scatter graph.

Middle

11+1 × ¼

=12 × ¼

=3 lower value=0

Interquartile range =1 - 0= 1

Here is another cumulative frequency table for the engine size 1.6

NO | Price | Frequency | Mid point | F x x | Cumulative frequency |

0 | 0>p>3000 | 3 | 1500 | 4500 | 3 |

1 | 3000>p>6000 | 4 | 4500 | 18000 | 3+4=7 |

2 | 6000>p>9000 | 2 | 7500 | 1500 | 7+2=9 |

3 | 9000>p>12000 | 0 | 10500 | 0 | 9 |

- Median

Median=Total +1 ÷ 2

9+1 ÷ 2

10 ÷2 = 5

INTER QUARTILE

Inter quartile range = upper value – Lower value

- Upper value= Total +1 × ¾

= 9+1 × ¾

= 10 × ¾

= 7.5 upper value=2

- Lower value= total + 1 × ¼

9+1 × ¼

=10 × ¼

=2.5 Lower value=0

Inter quartile range=2 - 0 =2

My third table is for the engine size 1.8. As my database contains 48 cars I find it difficult to have another widely spread engine like 1.4 and therefore I decided to use 1.8.

NO | Price | Frequency | Mid point | F x x | Cumulative frequency |

0 | 0>p>3000 | 1 | 1500 | 1500 | 1 |

1 | 3000>p>6000 | 2 | 4500 | 9000 | 1+2=3 |

2 | 6000>p>9000 | 2 | 7500 | 15000 | 3+2=5 |

3 | 9000>p>12000 | 0 | 10500 | 0 |

- Median

Median=Total +1 ÷ 2

5+1 ÷ 2

6 ÷2 = 3

INTER QUARTILE

Inter quartile range = upper value – Lower value

Upper value= Total+1 × ¾

= 5+1 × ¾

= 6 × ¾

= 4.5 upper value=2

Lower value= total + 1 × ¼

5+1 × ¼

=6 × ¼

=1.5 Lower value=1

Inter quartile = Upper value – lower quartile

2 – 1= 1

My second comparison is between age and prices. In order to find out what effect has age on second hand car prices I have decide to use graphs to compare them. I have chosen scatter graph for this comparison.

The graph below shows the result of my comparison.

The result above shows, as the age of the car increases the price decrease. This graph is a negative correlation graph because the car price decreases. The result above shows that age has influence on second hand car prices and age is considered as a key factor when you purchase it. The result which been circled is different from other results. The

Conclusion

In my investigation I have found that the age affects the second hand price the most since the correlation was strong and there were fewer outliers in the scatter graphs. This is followed by mileage as identical correlations were found and fewer outliers. The least most influential factor to the second hand price of the cars will be the engine size, as it had the most outliers and the graph correlations were not the same for each car make. This means that my hypothesis was incorrect because the mileage follows the age.

If I had additional time I would have used standard deviation which measure the spread and results are more reliable. I also would have proved using coefficient of covariance that age is the factor that affects the second hand price the most. Coefficient of covariance or r gives a value which can terminate which factor is most important. If r = +1, this indicates the correlation is positive. If the value of r is close to +1 then that means the correlation is stronger that the value that is away from +1. The same thing is with -1 which indicates that the correlation is negative. So the closer the value of r is to -1, the stronger the negative correlation. I would’ve used this method to find the values of r for mileage, age and engine size for all four makes. This would have proved which factor influences the second hand price of a car the most.

If I had used more data for this investigation, then the results would have been more concise and reliable. Also, the gradients of the scatter graphs would have been clearer and so would the box plots.

This student written piece of work is one of many that can be found in our GCSE Miscellaneous section.

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