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  • Level: GCSE
  • Subject: Maths
  • Word count: 3106

Statistics: Factors Affecting the Price of Used Cars

Extracts from this document...

Introduction

Statistics Coursework

Factors Affecting the Price of Used Cars

Aim: The aim of my investigation in this coursework is to find out if the factors, age and mileage affect the price of used cars and to what extent.

Introduction:

I am going to investigate the factors that affect the price of used cars. Many previous statistics collected by other people state that the age and mileage of used cars affect its price the most. Because of this, I want to investigate these factors to see if it is true or not therefore, I will not investigate any other factors such as make, model, fuel, colour, engine size, previous owners and tax. My investigation will help people find a good deal when buying a used car because they will know what decreases the price and roughly how much a used car should cost. Furthermore, I want to buy a car after I have passed my driving test so the results I get after I carry out my statistical project will help me save money when buying a car because I will be able to determine which car is good value for its price.

I am going to get my data of used cars from a primary source to carry out my investigation. I am going to go on a car website selling used cars to collect the data I need.

...read more.

Middle

79 159

77 980

71 074

68 838

68 446

54 848

52 329

51 580

25 925

Price (£)

10 999

10 799

10 599

9 499

8 999

8 799

8 499

7 999

7 599

7 499


I put my data in order if size so it is easier when making calculations such as the median. I didn’t include the year because they are all the same so the results I get will be reliable.

image19.pngimage21.png

image00.png

I worked out the mean of my data because it is usually the most representative and because it uses all the data. However, it may be distorted by outliers. I also worked out the median because it is not distorted by outliers. However, it is not always a good representation of the data so I will use it together with the range and interquartile range to make it more useful. I can’t find the mode because all of the data is different. There isn’t one that is more common than others.

image11.png

I calculated the range, interquartile range and the D8 – D2 decile range to see the spread of the data. I calculated the interquartile range because the range can be affected by extreme values as it only takes the difference between the highest and lowest number. The interquartile range tells me the range of the middle 50% of the data which is where most of the activity’s going on. I calculated the D8 – D2 decile range because it gives me the range of the middle 80% of the data which ignores any outliers. I did the decile range even though I did the interquartile range because the interquartile range might be cutting too much of the data away.

For the mileage, the range is very high and the interquartile range and decile range is much lower. This means there are some high values. The interquartile range and the decile range are quite close together so they give me a more realistic idea of the spread. For the price, the ranges are quite consistent so there shouldn’t be any extreme values.

Mileage standard deviation

x

x2

71,074

5,051,513,476

68,446

4,684,854,916

54,848

3,008,303,104

25,925

672,105,625

51,580

2,660,496,400

89,442

7,999,871,364

79,159

6,266,147,281

77,980

6,080,880,400

52,329

2,738,324,241

68,838

4,738,670,244

Totals

Σx = 639,621

Σ x2=43,901,167,051

image22.pngimage23.pngimage24.png

The standard deviation of mileage is very high which means the mileage data is more spread out. An advantage of the standard deviation over the ranges is that it uses all the data.

Price Standard Deviation

x

x2

£8,999

80,982,001

£9,499

90,231,001

£10,599

112,338,801

£10,799

116,618,401

£10,999

120,978,001

£7,499

56,235,001

£7,599

57,744,801

£7,999

63,984,001

£8,499

72,233,001

£8,799

77,422,401

Totals

Σx = 91,290

Σ x2=848,767,410

image25.pngimage26.pngimage23.png

image16.png

The standard deviation of the price data is quite small so the data isn’t very spread out.

To prove or disprove my hypothesis, I am going to look at the correlation between the mileage and price of the BMW cars I have in my data. To do this, I am going to use Spearman’s co-efficient rank of correlation and a scatter graph.

image27.png

image28.png

image30.png

I worked out Spearman’s co-efficient rank of correlation so I can know how well ordered the data is. Both the rank of correlation and scatter graph shows that there is a strong negative correlation between the price and mileage of cars. The strong negative correlation of -0.855 shows that as the mileage increases, the price decreases.

image31.pngimage32.png

image33.png

image34.png

image35.png

image36.png

image37.pngimage38.png

image39.pngimage43.pngimage42.pngimage41.png

image46.pngimage45.pngimage44.png

Year

Mileage

Price (£)

2005

89,547

13,999

2005

82,384

13,899

2005

81,704

13,699

2004

80,851

12,499

2004

50,063

12,299

2004

49,285

11,999

2003

46,367

10,499

2003

34,436

10,199

2003

32,758

9,999

2002

32,541

9,299

...read more.

Conclusion

For my project, I think my sample size was too small. I could’ve went to a different car company that’ has a bigger amount of cars for me to use. If I used more cars for my project, my results are likely to be more accurate. Also, I could’ve got a bigger range of cars because the prices of cars of my data are quite low. I could’ve got a very expensive type of car and see how much that decreases compared to a cheaper car. Furthermore, I could’ve got data on a vintage car which the price increases as the age increases. This would’ve shown a big difference compared to the cars that I’ve done, therefore, the results I obtained in this project should not be used to estimate prices of other cars. It should be used for the type of car I used or a car in the price range that I used.

To improve my project, I could expand it by using data on different cars with a higher price and a lower price. I could also collect data on vintage cars to use for my project.

...read more.

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