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• Level: GCSE
• Subject: Maths
• Word count: 2634

# My maths coursework is based on a spreadsheet with information about cars. I am going to study the data and answer the question - In general does the age of second hand cars affect the price?

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Introduction

GCSE Maths Coursework – Statistics

My maths coursework is based on a spreadsheet with information about cars.  I am going to study the data and answer the following questions: -

• In general does the age of second hand cars affect the price?
• Does the mileage of second hand cars affect the price?
• Does the size of the engine on second hand cars affect the price?
• The average cost of Vauxhall cars compared to Ford cars.

In general does the age of second hand cars affect the price?

Plan

I am going to find out whether the age of second hand cars affects the price.

I am going to use all the data in the spreadsheet as there are only a hundred pieces.  This will make my results as accurate as possible.

Firstly I am going to separate the age and price columns from the rest of the spreadsheet.  Then I will sort the data into age groups and take the average of each group.  The averages of each age group will be then put into a table and on a line of best fit.  I am going to use the averages because this is the best way to display the data.  All of the data from each category (Make of car) will be used to work out the averages, as there isn’t enough data in each category to take a sample.

Collecting, Processing and Representing

Middle

11

1495

15

400

The information is shown below in the form of a line graph.  I chose to use a line graph as this is the best way to display the data as it shows patterns and trends.

I have removed the anomalous result and redrawn the graph.

I have also plotted all of the results on a scatter diagram shown below.

Interpret and discuss

A line graph was drawn using the averages of the different years.

There is an anomalous result at eight years, as a Bentley car was particularly expensive and this is making the average much higher.

The line graph shows that generally the older a car get the less it costs.

The line graph shows a general trend in the results but isn’t that accurate.  So I plotted all the data into a scatter diagram with line of best fit.  The three anomalous results where removed from the data before the diagram was drawn.

If I was to repeat this question I would use all the data the first time or use a larger random sample.

I think the scatter diagram was particularly good although the line graph shows trends and patterns in the data, but isn’t very accurate.

Does the mileage of second hand cars affect the price?

Plan

I am going to find out whether the mileage of second hand cars affects the price.

Firstly I will separate the price and mileage from the rest of the data.

I will take a random sample of the data using the random number generator on the calculator, thirty random numbers will be generated then the corresponding cars will be separated from the data.  I have chosen thirty cars because this is an adequate sample approximately one third of the data.

I am then going to use this data to plot a scatter diagram.  A line of best fit will then be drawn in.

Collecting, Processing and Representing

Below is a table showing the price and the mileage of all the cars.

 Mileage Price 30000 6999 30000 6595 30000 4999 40000 1595 49000 3795 43000 895 13000 45000 103000 3995 43000 3191 21000 4976 42000 5995 38000 3769 45000 795 24000 4995 68000 1595 70000 7999 33000 2495 20000 1995 47000 1995 50000 1495 14730 6895 58000 12999 52000 2748 49000 2450

The following cars don’t have the mileage stated so will have to be left out of my results.

 400 1295 6250

Conclusion

6595

4

19589

Vauxhall

7499

4

27088

Vauxhall

6499

4

33587

Vauxhall

4976

4

38563

Vauxhall

4995

5

43558

Vauxhall

2900

6

46458

Vauxhall

3495

6

49953

Vauxhall

6995

6

56948

Vauxhall

3191

6

60139

Vauxhall

1000

10

61139

Vauxhall

850

10

61989

Total

61989

61989

 Ford Vauxhall Mean - 4288 Mean - 4768 Lower Quartile – 2.2 Lower Quartile – 2.6 Upper Quartile - 5 Upper Quartile – 5.4 Modal Class - 2 Modal Class - 2

Interpret and discuss

Ford and Vauxhall were the two most popular makes of car as shown above in the doughnut diagram.  So I used these in the comparison.

A sampling method wasn’t used as there was only a small amount of data for each make of car.

The cumulative frequency diagram shows that generally Ford cars are a similar price to Vauxhalls.  On some points of the Cumulative frequency Diagram Vauxhall is higher than Ford but at some points it is the opposite.

The box and whisker plot shows that the mean of the cars is very similar.  There is a greater range of data about Ford cars, although it isn’t much different.  Vauxhalls Mean, Lower Quartile and Upper Quartile is slightly higher than Fords but not significantly enough to make a comparison.

The scatter diagram comparing the two makes shows they are very similar.

It isn’t possible to say which car is the most expensive so I have come to the conclusion that:

Generally the price second hand Ford and Vauxhall cars is very similar, there aren’t any major differences in price.

If I was to repeat this question I wouldn’t do a scatter diagram as it is very difficult to draw accurate lines of best fit.

I am particularly proud of the Cumulative Frequency Diagram which compares the two sets of data.

Dale Irving, 11M

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