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  • Level: GCSE
  • Subject: Maths
  • Word count: 3774

The aim of this experiment is: To observe how differences from car to car effects the second hand value e.g. colour, make, mileage, engine size length of MOT and the number of seats.

Extracts from this document...

Introduction

Plan

The aim of this experiment is:

  • To observe how differences from car to car effects the second hand value e.g. colour, make, mileage, engine size length of MOT and the number of seats.
  • To do this I will display the data in a wide range of graphs and charts from which I will make comparisons.  
  • To select the data in the first place I will use a range of sampling methods. Systematic sampling an example of this is selecting 10% of the data by taking every tenth value etc.  For this method to work the data must be arranged in an unbiased way in no particular order (random).  Attribute sampling this is were the data chosen would depend on a completely different factor e.g. if I want to select the data for mileage I may use red and blue cars, as this doesn’t affect the data in any way.  This has one set back as sometimes the other variable may have an effect on the data without you knowing but this is a good sampling method to use as I have lots of sets of data which otherwise would not be used.  Stratified sampling this is were the data is put into sub groups for example if there are 3 times more cars that are diesel than petrol there should be 3 times more in the sample.  Random sampling in a random sample every set of data has a chance of being used to do this data values could be drawn out of a hat or given a number and select a number at random.  Quota sampling this is were the data used has to be from a certain sub group i.e. Vauxhall.  Cluster sampling the population is divided into small groups called clusters then one or more of these clusters are selected.  Stratified random sampling this is obtained by separating the data in to appropriate categories called stratas e.g. by mileage.  Then find out what percentage of all the data Is in each  strata then selecting a random sample form each sample in proportion to its size.
  • When the data is chosen by whichever method it will be placed in a table an then represented on a graph the graphs I will use are: scatter graph, cumulative frequency curve.
  • On my scatter graph I will work out and draw the line of best fit going through the mean and work out the least squares regression line, standard deviation, and the spearmans rank correlation coefficient all these methods will be explained further in my explanation page.
  • From the cumulative frequency the median and upper and lower quartiles will be worked out these values will then be displayed in box plots and then all the data will be analyzed  see explanation for further details
...read more.

Middle

44

0-5

40000

70

48

0-5

49000

59

50

0-5

32400

54

53

0-5

38000

60

55

0-5

13000

43

60

0-5

66000

81

75

0-5

96000

88

84

0-5

21000

37

94

0-5

52000

64

3

5-10

20000

57

10

5-10

27000

44

17

5-10

33000

62

49

5-10

14730

50

63

5-10

35000

57

64

5-10

7200

39

93

5-10

63000

63

69

10-15

2000

23

71

10-15

40500

50

73

15+

46000

41

Analysis of my graph and data to show the link between mileage and % value decrease.

The product moment correlation coefficient is +0.859 (3dp) the working out is on the hand written sheet, which follows.

This tells us that the 2 variables have a strong positive correlation +1 is a perfect positive correlation and all the points will lie on the line of best fit.  If this is the case as my graph shows many of the points lie near the line of best fit but few are actually on the line.  This is because my data is not perfectly correlated.  This is because not all cars decrease in value by the same amount after travelling the same amount of miles.  Some cars retain their value longer than others and some lose their value after only a few miles.  This could be because some cars wear better or there is more of a demand for that particular make or model.   My graph has a fairly steep line of best-fit going upwards and to the right this tells us that the data is positively correlated.  The fact that the line of best fit is a straight line tells us that the link between mileage and value decrease is constant i.e. it doesn’t curve down towards the end which would indicate extreme changes in value decrease after 80 000 miles.  

The least squares regression equation has shown that the equation for the line of best fit is y= 1207x-30581 my working out follows.

The line is similar to my hand drawn line of best fit but it is slightly steeper this tells me that it is difficult to draw lines of best fit accurately by hand.  The line of best fit constructed using the equation y= 1207x-30157 tells me pretty much the same as my hand drawn line of best fit told me.  Except I now know the gradient of the line of best fit is 1206 before I estimated it at about 1545 I got this value by taking 2 points lying on my hand drawn line of best fit and using the formula change in y/change in x.  Full working out follows.

Cumulative frequency Results

A cumulative frequency table for cars between 0 and 3 years old.

% decrease in value

frequency

≤10

0

≤20

1

≤30

3

≤40

7

≤50

13

≤60

18

≤70

20

≤80

20

≤90

20

≤100

20

A cumulative frequency table for cars between 3 and 6 years old.

% decrease in value

frequency

≤10

0

≤20

0

≤30

0

≤40

0

≤50

4

≤60

8

≤70

15

≤80

19

≤90

20

≤100

20

...read more.

Conclusion

Evaluation

I have found that all the variables I chose to use affected the % value decrease to varying degrees my scatter graph showed me that mileage and % value decrease correlate strongly and positively getting a value of +0.859.  my cumulative frequency showed me that the older a car gets the cheaper it becomes it is not quite as strongly correlated as the scatter graph but there Is a definite link between age and % value decrease.  To obtain better results I would like to use a bigger sample of data this decreases the chance of inaccuracies occurring due to freak sets of data or anomalous results.  Also there are other factors that need to be considered the state of the economy would affect the amount people can afford to pay for cars this could change the starting value of a car.  Meaning the second hand value of a car is distorted the war on Iraq which is currently in progress has shown that people are worried about the state of the economy and are spending less.  Things like this can mean that there are good and bad years for car sales and a car 10 years old may have a smaller % value decrease than a much younger one.

...read more.

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