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  • Level: GCSE
  • Subject: Maths
  • Word count: 3225

Gary's Car Sales.

Extracts from this document...

Introduction


Introductionimage00.png

This assignment was completed on a PC, written with MS Word and the graphs, charts and tables included where created using MS Excel and pasted into this document.

Firstly the car data from the assignment was entered into Excel. This then allowed tables, charts & graphs to be created that could represent the various comparisons to be made.

Car No.

Price

Age

(Years)

Make

Cost When New

Mileage

Engine Size

(Litres)

1

£6,970.00

3

Ford

£11,600.00

24000

1.6

2

£3,350.00

7

Peugeot

£7,100.00

85000

1.1

3

£3,995.00

60

Ford

£138,000.00

52000

2.0

4

£5,300.00

6

Vauxhall

£16,300.00

70000

2.0

5

£6,500.00

3

Fiat

£8,700.00

24000

1.2

6

£1,500.00

9

Vauxhall

£8,700.00

82000

1.6

7

£995.00

9

Ford

£8,500.00

102000

1.8

8

£3,000.00

7

Vauxhall

£10,400.00

63000

1.7

9

£7,495.00

1

Vauxhall

£9,770.00

8000

1.4

10

£850.00

10

Ford

£7,540.00

124000

1.6

11

£5,595.00

4

Ford

£11,000.00

41000

1.6

12

£4,995.00

3

Ford

£9,880.00

34000

1.4

13

£5,595.00

4

Ford

£14,000.00

55000

1.6

14

£4,995.00

4

Rover

£11,500.00

40000

1.4

15

£2,600.00

7

Rover

£12,000.00

82000

1.6

16

£1,000.00

10

Peugeot

£6,200.00

119000

1.1

17

£750.00

11

Peugeot

£5,100.00

96000

1.0

18

£1,350.00

8

Ford

£9,140.00

108000

1.6

19

£2,950.00

8

Ford

£17,750.00

96000

2.9

20

£3,250.00

7

Vauxhall

£9,990.00

86000

1.6

21

£5,650.00

3

Vauxhall

£11,150.00

34000

1.6

22

£4,600.00

2

Rover

£7,300.00

17000

1.1

23

£5,400.00

1

Rover

£7,300.00

11000

1.1

24

£4,800.00

1

Rover

£7,300.00

26000

1.1

25

£2,700.00

5

Fiat

£13,000.00

51000

2.0

26

£11,000.00

1

Peugeot

£13,800.00

9000

1.8

27

£2,800.00

5

Fiat

£6,500.00

43000

1.0

28

£8,000.00

4

Rover

£21,000.00

142000

2.3

29

£6,495.00

2

Ford

£8,800.00

23000

1.3

30

£4,050.00

4

Ford

£8,400.00

48000

1.3

31

£6,300.00

2

Ford

£10,300.00

26000

1.3

32

£4,100.00

4

Vauxhall

£8,900.00

37000

1.3

33

£6,600.00

1

Vauxhall

£8,500.00

9000

1.3

34

£7,800.00

1

Peugeot

£10,500.00

13000

1.4

35

£8,700.00

3

Vauxhall

£16,000.00

42000

2.0

36

£2,000.00

7

Peugeot

£8,300.00

65000

1.4


Investigation

Representing the information

Firstly a bar chart was created to graphically represent the price of each of the 36 cars in stock:image01.png

The table below was constructed to allow a bar chart displaying Price, Cost When New & Difference (Price subtracted from Cost When New) to be made. The cars on the chart are ordered by age.  The Bar chart can be found on the next page.

  Car No.

Age (yrs)

Price

Cost When New

Difference

9

1

£7,495.00

£9,770.00

£2,275.00

23

1

£5,400.00

£7,300.00

£1,900.00

24

1

£4,800.00

£7,300.00

£2,500.00

26

1

£11,000.00

£13,800.00

£2,800.00

33

1

£6,600.00

£8,500.00

£1,900.00

34

1

£7,800.00

£10,500.00

£2,700.00

22

2

£4,600.00

£7,300.00

£2,700.00

29

2

£6,495.00

£8,800.00

£2,305.00

31

2

£6,300.00

£10,300.00

£4,000.00

1

3

£6,970.00

£11,600.00

£4,630.00

5

3

£6,500.00

£8,700.00

£2,200.00

12

3

£4,995.00

£9,880.00

£4,885.00

21

3

£5,650.00

£11,150.00

£5,500.00

35

3

£8,700.00

£16,000.00

£7,300.00

11

4

£5,595.00

£11,000.00

£5,405.00

13

4

£5,595.00

£14,000.00

£8,405.00

14

4

£4,995.00

£11,500.00

£6,505.00

28

4

£8,000.00

£21,000.00

£13,000.00

30

4

£4,050.00

£8,400.00

£4,350.00

32

4

£4,100.00

£8,900.00

£4,800.00

25

5

£2,700.00

£13,000.00

£10,300.00

27

5

£2,800.00

£6,500.00

£3,700.00

4

6

£5,300.00

£16,300.00

£11,000.00

2

7

£3,350.00

£7,100.00

£3,750.00

8

7

£3,000.00

£10,400.00

£7,400.00

15

7

£2,600.00

£12,000.00

£9,400.00

20

7

£3,250.00

£9,990.00

£6,740.00

36

7

£2,000.00

£8,300.00

£6,300.00

18

8

£1,350.00

£9,140.00

£7,790.00

19

8

£2,950.00

£17,750.00

£14,800.00

6

9

£1,500.00

£8,700.00

£7,200.00

7

9

£995.00

£8,500.00

£7,505.00

10

10

£850.00

£7,540.00

£6,690.00

16

10

£1,000.00

£6,200.00

£5,200.00

17

11

£750.00

£5,100.00

£4,350.00

3

60

£3,995.00

£138,000.00

£134,005.00


image02.png


Averages

...read more.

Middle

1

£6,970.00

3

£3,995.00

7

£995.00

10

£850.00

11

£5,595.00

12

£4,995.00

13

£5,595.00

18

£1,350.00

19

£2,950.00

29

£6,495.00

30

£4,050.00

31

£6,300.00

Total

£50,140.00

The mean value of Ford cars in stock = £50,140 divided by 12 = £4,178.33

Car No.

Peugeot

2

£3,350.00

16

£1,000.00

17

£750.00

26

£11,000.00

34

£7,800.00

36

£2,000.00

Total

£25,900.00

The mean value of Peugeot cars in stock = £25,900 divided by 6 = £4,316.67

Car No.

Rover

14

£4,995.00

15

£2,600.00

22

£4,600.00

23

£5,400.00

24

£4,800.00

28

£8,000.00

Total

£30,395.00

The mean value of Rover cars in stock = £30,395 divided by 6 =  £5,065.83

Car No.

Vauxhall

4

£5,300.00

6

£1,500.00

8

£3,000.00

9

£7,495.00

20

£3,250.00

21

£5,650.00

32

£4,100.00

33

£6,600.00

35

£8,700.00

Total

£45,595.00

The mean value of Vauxhall cars in stock = £45,595 divided by 9 = £5,066.11

The total value of stock is £164,030

The mean value of the total stock  = £164,030 divided by 36 = £4,556.39

The median value of the total stock was then calculated using the table of ordered prices below:

Car No.

Price

17

£750.00

10

£850.00

7

£995.00

16

£1,000.00

18

£1,350.00

6

£1,500.00

36

£2,000.00

15

£2,600.00

25

£2,700.00

27

£2,800.00

19

£2,950.00

8

£3,000.00

20

£3,250.00

2

£3,350.00

3

£3,995.00

30

£4,050.00

32

£4,100.00

22

£4,600.00

24

£4,800.00

12

£4,995.00

14

£4,995.00

4

£5,300.00

23

£5,400.00

11

£5,595.00

13

£5,595.00

21

£5,650.00

31

£6,300.00

29

£6,495.00

5

£6,500.00

33

£6,600.00

1

£6,970.00

9

£7,495.00

34

£7,800.00

28

£8,000.00

35

£8,700.00

26

£11,000.00

Because there isn’t a middle value (due to the fact there is 36 cars) the two middle values are added together and divided by 2. The two values to be used are 18th & 19th in the ordered list, car 22 (£4,600) & car 24 (£4,800).

The median value of the total stock = (£4,600 + £4,800) divided by 2 = £4,700

The mode value (most frequent) of the total stock  = £5,595 & £4,995 (2 each).

The range of the total stock =

Highest value (£750) – Lowest value (£11,000) = £10,250

The percentages of stock by make where then calculated:

Fiat £12,000 as a percentage of £164,030 =

(£12,000 divided by £164,030) x 100 = 7.3%

Ford £50,140 as a percentage of £164,030 =

(£50,140 divided by £164,030) x 100 = 30.5%

Peugeot £25,900 as a percentage of £164,030 =

(£25,900 divided by £164,030) x 100 = 15.8%

Rover  £30,395 as a percentage of £164,030 =

(£30,395 divided by £164,030) x 100 = 18.6%

Vauxhall £45,595 as a percentage of £164,030 =

(£45,595 divided by £164,030) x 100 = 27.8%

The information above was then used to construct a pie chart that represents the percentage of stock by make:


Identifying Trendsimage03.png

Below various attributes of each car are compared to identify any trends in the price of the various cars held in stock.

Mileage v Age.

The table below shows the data used to plot the scatter chart of Mileage v Age. Car 3 was exclude from the chart as its excessive age would skew the age scale. The scatter chart has a linear trend line drawn to show the trend that older cars tend to have higher mileage.

Car No.

Age (yrs)

Mileage

1

3

24000

2

7

85000

3

60

52000

4

6

70000

5

3

24000

6

9

82000

7

9

102000

8

7

63000

9

1

8000

10

10

124000

11

4

41000

12

3

34000

13

4

55000

14

4

40000

15

7

82000

16

10

119000

17

11

96000

18

8

108000

19

8

96000

20

7

86000

21

3

34000

22

2

17000

23

1

11000

24

1

26000

25

5

51000

26

1

9000

27

5

43000

28

4

142000

29

2

23000

30

4

48000

31

2

26000

32

4

37000

33

1

9000

34

1

13000

35

3

42000

36

7

65000

...read more.

Conclusion

image06.png

Depreciation per Year v Age:

Depreciation per Year has been calculated by dividing % depreciation by the age of a car, the table below displays the results.

Car No.

Age (yrs)

Make

% Depreciation

%Depreciation per Yr

1

3

Ford

39.91%

13.30%

2

7

Peugeot

52.82%

7.55%

3

60

Ford

97.11%

1.62%

4

6

Vauxhall

67.48%

11.25%

5

3

Fiat

25.29%

8.43%

6

9

Vauxhall

82.76%

9.20%

7

9

Ford

88.29%

9.81%

8

7

Vauxhall

71.15%

10.16%

9

1

Vauxhall

23.29%

23.29%

10

10

Ford

88.73%

8.87%

11

4

Ford

49.14%

12.28%

12

3

Ford

49.44%

16.48%

13

4

Ford

60.04%

15.01%

14

4

Rover

56.57%

14.14%

15

7

Rover

78.33%

11.19%

16

10

Peugeot

83.87%

8.39%

17

11

Peugeot

85.29%

7.75%

18

8

Ford

85.23%

10.65%

19

8

Ford

83.38%

10.42%

20

7

Vauxhall

67.47%

9.64%

21

3

Vauxhall

49.33%

16.44%

22

2

Rover

36.99%

18.49%

23

1

Rover

26.03%

26.03%

24

1

Rover

34.25%

34.25%

25

5

Fiat

79.23%

15.85%

26

1

Peugeot

20.29%

20.29%

27

5

Fiat

56.92%

11.38%

28

4

Rover

61.90%

15.48%

29

2

Ford

26.19%

13.10%

30

4

Ford

51.79%

12.95%

31

2

Ford

38.83%

19.42%

32

4

Vauxhall

53.93%

13.48%

33

1

Vauxhall

22.35%

22.35%

34

1

Peugeot

25.71%

25.71%

35

3

Vauxhall

45.63%

15.21%

36

7

Peugeot

75.90%

10.84%

The scatter graph below shows Depreciation Per Year v Age. A trend line has been added.

image07.png

Depreciation by Make

The table below shows % Depreciation per Year ordered by Make

Car No.

Make

%Depreciation per Yr

5

Fiat

8.43%

25

Fiat

15.85%

27

Fiat

11.38%

1

Ford

13.30%

3

Ford

1.62%

7

Ford

9.81%

10

Ford

8.87%

11

Ford

12.28%

12

Ford

16.48%

13

Ford

15.01%

18

Ford

10.65%

19

Ford

10.42%

29

Ford

13.10%

30

Ford

12.95%

31

Ford

19.42%

2

Peugeot

7.55%

16

Peugeot

8.39%

17

Peugeot

7.75%

26

Peugeot

20.29%

34

Peugeot

25.71%

36

Peugeot

10.84%

14

Rover

14.14%

15

Rover

11.19%

22

Rover

18.49%

23

Rover

26.03%

24

Rover

34.25%

28

Rover

15.48%

4

Vauxhall

11.25%

6

Vauxhall

9.20%

8

Vauxhall

10.16%

9

Vauxhall

23.29%

20

Vauxhall

9.64%

21

Vauxhall

16.44%

32

Vauxhall

13.48%

33

Vauxhall

22.35%

35

Vauxhall

15.21%

The mean average % depreciation for the stock of cars is 14.19%.

The mean average % depreciation per year for each Make is as follows:

Fiat

(8.43 + 15.85 + 11.38) divided by 3

=11.89%

Ford

(13.30 + 1.62 + 9.81 + 8.87 + 12.28 + 16.48 + 15.01 + 10.65 + 10.42 + 13.10 + 12.95 + 19.42) divided by 12

=11.99%

Peugeot

(7.55 + 8.39 + 7.75 + 20.29 + 25.71 + 10.84) divided by 6

=13.42%

Rover

(14.14 + 11.19 + 18.49 + 26.03 + 34.25 + 15.48) divided by 6

=19.93%

Vauxhall

(11.25 + 9.20 + 10.16 + 23.29 + 9.64 + 16.44 + 13.48 + 22.35 + 15.21) divided by 9

=23.44%

The bar chart shows the Mean % Depreciation per year by Make of car.

image08.png

...read more.

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