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• Level: GCSE
• Subject: Maths
• Word count: 8022

# The aim of this investigation is to find out what influences the price of second hand cars.

Extracts from this document...

Introduction

Inderpal Singh

Heston Community School

MATHEMATICS COURSEWORK:

Statistical data

Use the information to investigate what influences the price of a second hand car

Aim

The aim of this investigation is to find out what influences the price of second hand cars. (used cars)

Introduction

## Hypothesis

The sample provided, includes a list of 100 cars that shows quantitative and qualitative data, such as Second Hand Price, Engine Size and Colour.

To obtain my hypothesis, I carried out research in a car magazine called ‘LOOT’ and a website: www.autotrader.co.uk From this I found out that the most common cars reflected my sample and this was also a good indication of cars on the current market today.

The magazine and website research gave me quantitative results.

Therefore, my hypothesis and what I will investigate from this is:

“The older the car in age and the more owners it has, the more cheaply the second hand price value is going to be.”

Also, I take into consideration that, “The less mileage the car has, the better condition and more expensive the car is. This more mileage the car has, the more likely chance of it being a cheap, second hand car.”

I chosen this as my hypothesis because, in reality that is what determines the price of car,

For example,

If a new car in age had a lot of owners, it would vary the second hand price of the car.

This is compared to a the same car, but with fewer owners, it will make the second hand price a lot more expensive than the new car with a lot of owners.

## Method

To achieve my hypothesis, I am going to compare:

- The Make of the Cars, Price When New, The Age of The Cars, The Mileage the Cars Travel & How Many Owners the Cars has.

Middle

£13,850

£6,895

50.2166065

£6,955

Daewoo

Lanos

£11,225

£5,999

46.55679287

£5,226

Daewoo

Lanos

£9,525

£4,395

53.85826772

£5,130

Fiat

Uno

£6,864

£1,495

78.21969697

£5,369

Fiat

Tipo

£8,272

£1,500

81.86653772

£6,772

Fiat

Punto

£7,864

£4,500

42.77721261

£3,364

Fiat

Bravo

£10,954

£6,795

37.96786562

£4,159

Fiat

Bravo

£10,810

£4,995

53.79278446

£5,815

Fiat

Punto

£7,518

£3,769

49.8669859

£3,749

Fiat

Tempra

£10,423

£1,295

87.57555406

£9,128

Fiat

Bravo

£10,351

£3,495

66.23514636

£6,856

Fiat

Punto

£8,601

£3,995

53.55191257

£4,606

Fiat

Cinquecento

£6,009

£1,995

66.7998003

£4,014

Ford

Puma

£13,230

£8,250

37.64172336

£4,980

Ford

Mondeo

£17,780

£7,995

55.03374578

£9,785

Ford

Escort

£15,405

£3,995

74.06686141

£11,410

Ford

Orion

£16,000

£7,999

50.00625

£8,001

Ford

Escort

£8,785

£1,595

81.84405236

£7,190

Ford

Fiesta LX

£8,748

£1,995

77.19478738

£6,753

Ford

Escort Duet

£9,105

£2,300

74.73915431

£6,805

Ford

Escort

£12,125

£4,295

64.57731959

£7,830

Ford

Escort

£11,800

£4,700

60.16949153

£7,100

Ford

Fiesta

£8,680

£3,200

63.13364055

£5,480

Ford

Fiesta

£6,590

£1,664

74.74962064

£4,926

Ford

Focus

£14,505

£8,800

39.33126508

£5,705

Ford

Escort

£13,183

£3,495

73.48858378

£9,688

Ford

Fiesta

£7,310

£1,050

85.63611491

£6,260

Ford

Escort

£9,995

£2,995

70.03501751

£7,000

Honda

Civic

£12,895

£7,995

37.99922451

£4,900

Hyundai

Accent

£6,899

£2,800

59.41440789

£4,099

Hyundai

Sonnata

£11,598

£1,195

89.6964994

£10,403

Land rover

Discovery

£27,855

£13,995

49.75767367

£13,860

Mazda

Pegasus

£10,420

£2,495

76.05566219

£7,925

Mercedes

A140 Classic

£14,425

£10,999

23.75043328

£3,426

Mercedes

AvantGarde

£17,915

£11,750

34.41250349

£6,165

Mercedes

Elegance

£26,425

£17,500

33.77483444

£8,925

Mitsubishi

Carisma GDI

£14,875

£5,999

59.67058824

£8,876

Mitsubishi

Carisma

£15,800

£5,999

62.03164557

£9,801

Nissan

Micra

£7,995

£3,999

49.98123827

£3,996

Nissan

Micra

£6,295

£1,795

71.4853058

£4,500

Nissan

Micra

£5,340

£1,595

70.13108614

£3,745

Nissan

Sunny

£7,799

£2,595

66.7265034

£5,204

Nissan

Almera

£12,590

£4,300

65.84590945

£8,290

Nissan

Primera

£13,355

£2,574

80.72631973

£10,781

Peugeot

206

£9,125

£7,500

17.80821918

£1,625

Peugeot

£7,600

£2,497

67.14473684

£5,103

Peugeot

306

£12,350

£3,995

67.65182186

£8,355

Peugeot

406LX

£13,975

£5795

58.53309481

£8,180

Peugeot

406

£17,490

£7500

57.11835334

£9,990

Porsche

Sport

£32,995

£13495

59.09986362

£19,500

Renault

Megane

£13,175

£6,999

46.87666034

£6,176

Renault

Megane

£13,610

£4,999

63.26965467

£8,611

Renault

Clio

£6,795

£1,995

70.6401766

£4,800

Renault

Clio

£7,403

£1,495

79.80548426

£5,908

Renault

19

£11,695

£2,748

76.50277897

£8,947

Rolls Royce

Silver Spirit

£94,651

£14,735

84.43228281

£79,916

Rover

820 SLi

£21,586

£3,795

82.41916057

£17,791

Rover

416i

£13,586

£3,795

72.06683351

£97,91

Rover

114 Sli

£8,595

£2,495

70.97149506

£61,00

Rover

Metro

£6,645

£895

86.53122649

£57,50

Rover

214i

£9,565

£1,700

82.22686879

£78,65

Rover

Metro

£5,495

£1,995

63.69426752

£35,00

Rover

623 Gsi

£22,980

£6,999

69.54308094

£15,981

Rover

623GSi

£24,086

£2,975

87.64842647

£21,111

Rover

620Si

£17,795

£3,400

80.89350941

£14,395

Rover

Club

£19,530

£14,999

23.20020481

£4,531

Rover

623 GSi

£24,086

£2,975

87.64842647

£21,111

Rover

416i

£14,486

£3,685

74.56164573

£10,801

Suzuki

Vitara

£10,800

£2,995

72.26851852

£7,805

Toyota

Corrolla

£13,800

£7,495

45.6884058

£6,305

Vauxhall

Tigra

£13,510

£7,499

44.49296817

£6,011

Vauxhall

Calibra

£18,675

£6,995

62.54350736

£11,680

Vauxhall

Astra

£14,325

£6,595

53.96160558

£7,730

Vauxhall

Corsa

£8,900

£4,995

43.87640449

£3,905

Vauxhall

Nova

£5,599

£1,000

82.1396678

£4,599

Vauxhall

Astra

£13,740

£2,900

78.8937409

£10,840

Vauxhall

Corsa

£7,840

£4,976

36.53061224

£2,864

Vauxhall

Corsa

£7,440

£3,495

53.02419355

£3,945

Vauxhall

Astra

£9,795

£3,191

67.42215416

£6,604

Vauxhall

Vectra

£13,435

£4,995

62.82098995

£8,440

Vauxhall

Vectra

£18,580

£7,999

56.94833154

£10,581

Vauxhall

Vectra

£18,140

£6,499

64.17309813

£11,641

Vauxhall

Cavalier

£10,150

£850

91.62561576

£9,300

Volkswagen

Golf

£12,999

£3,595

72.34402646

£9,404

Volkswagen

Golf

£9,524

£3,695

61.20327593

£5,829

Volkswagen

Golf GTi

£16,139

£6,995

56.65778549

£9,144

Volkswagen

Beetle

£14,950

£13,500

9.698996656

£1,450

Volkswagen

Polo

£9,960

£7,550

24.19678715

£2,410

Volkswagen

Polo

£8,710

£4,693

46.11940299

£4,017

From this the table showing price drop I can see that the majority of cars had a price drop of more than half from the original, price when new. This is probably due to the fact that the age of car affected how much the car’s value decreased by.

For example,

If it was a new car in age, i.e. 1 or 2 years old, the price of that car would not decrease as much as a car that was 9 years old for instance. The 9-year-old car would have a greater price drop. This is because, as the age increases, the value of the car will decrease

We can also see from the table, the Modal Price When New, Median Price When New and the Range of the Price When New.

The Modal Price When New is the value that occurs the most. This is from the car Rover 623Gsi, which is £24,086. This value appears twice in the table. Therefore, it is entitled as the Modal Price When New.

Furthermore, the Median is defined as:

“the middle value when the data is arranged in order of size.”

If there is an even number of values in the data, then the median is the mean of the middle two values.

This is calculated by making the table in numerical order by Price When New.

I then look for the middle value, as the total number of cars is 93. There cannot be two values in the data that require a mean.

£5,340 £5,495 £5,599 £5,715 £6,009 £6,295 £6,590 £6,645 £6,795 £6,864 £6,899 £7,310 £7,403 £7,440 £7,518 £7,600 £7,799 £7,840 £7,864 £7,995 £8,272 £8,595 £8,601 £8,680 £8,710 £8,748 £8,785 £8,900 £9,105 £9,125 £9,524 £9,525 £9,565 £9,795 £9,960 £9,995 £10,150 £10,351 £10,420 £10,423 £10,800 £10,810 £10,954 £11,225 £11,598 £11,695 £11,800 £12,125 £12,350 £12,590 £12,895 £12,999 £13,175 £13,183 £13,230 £13,355 £13,435 £13,510 £13,586 £13,610 £13,650 £13,740 £13,800 £13,850 £13,975 £14,065 £14,325 £14,425 £14,486 £14,505 £14,875 £14,950 £15,405 £15,800 £16,000 £16,139 £17,490 £17,780 £17,795 £17,915 £18,140 £18,580 £18,675 £19,530 £21,586 £22,980 £24,086 £24,086 £26,425 £27,855 £28,210 £32,995 £94,651

From the numerical data shown above, it is clear to me that, £11,800 is the Median value for Price When New.

Finally, to work out the Range of the Price When New, I look at the highest value in the data and subtract that from the lowest data.

In this case, it will be:

£94,651 - £5,340 = £89,311

GRAPH ANALYSIS

I put the price when new into interval values to present my graph.

As shown below:

TABLE SHOWING PRICE WHEN NEW INTERVALS AGAINST AVERAGE SECOND HAND PRICE

 Price When New Second Hand Price 0-4999 0 5000-5999 £1,521.25 6000-6999 £1,805.57 7000-7999 £3,152.89 8000-8999 £3,058.50 9000-9999 £4,165.75 10000-10999 £3,274.29 11000-11999 £3,660.50 12000-12999 £4,836.00 13000-13999 £5,591.23 14000-14999 £7,432.57 15000-15999 £4,997.00 16000-16999 £7,497.00 17000-17999 £7,661.25 18000-18999 £7,164.33 19000-19999 £14,999.00 21000-21999 £3,795.00 22000-22999 £6,999.00 24000-24999 £2,975.00 26000-26999 £17,500.00 27000-27999 £13,995.00 28000-28999 £5,995.00 32000-32999 £19,495.00 94000-94999 £14,735.00

I have chosen a scatter graph to represent this variable; to show the contrast between the price when new and the second hand price.

The scatter graph tells me that it has a low positive correlation from the line of best fit. This means that the graph has not got a strong relationship between the price when new and the second hand price. It also means that as data from one set increases, as does the data from the other set.

The points plotted are very close to the straight line (line of best fit). This shows a trend of strong evidence between the price when new and the second hand

PRICE WHEN NEW ANALYSIS

The New Price of Car shows me how much a car costs and how much it has decreased by to obtain the cost of the second hand price. It has shown me that the New Price effects the second hand price by how much the car’s value reduces.

As there were two identical values, this is then known as the mode or modal value.

The Modal value for the Price When New is £24,086

The median shows the middle number in the data, to give an estimate of what the car prices are like.

The Median value of Price When New is £11,800

The range shows the measure of spread, this is how close the data is in relation to the mean.

The Range of the Price When New is £89,311

AGE OF CAR

3.) The third variable that I think influences the price of a second hand car is the Age of a car, this is because, the age shows how old a car is in comparison to the second hand price.

In theory, a newer aged car would cost more than an older car, this is for the reason that, the older has lost its value of the years.

I am going to produce a table with my findings of how the age affects the second hand price and analyse the quantitative, numerical data in a bar graph format.

TABLE SHOWING THE AGE OF THE CARS IN COMPARISON TO THE AVERAGE SECOND HAND PRICE

 Age Frequency Second Hand Price 1 year 10 £9,883.20 2 years 9 £8,392.44 3 years 8 £5,529.00 4 years 11 £5,643.42 5 years 8 £4,406.00 6 years 18 £4,402.17 7 years 11 £2,186.82 8 years 9 £2,441.33 9 years 5 £4,318.80 10 years 3 £1,171.33

Conclusion

NUMBER OF OWNERS ANALYSIS

As you would expect, the more owners a car has, lower the value for the car is going to be.

This makes the car cheaper. Which would make it a right reason to sell the car.

Which makes number of owners a main factor in the influences of a second hand price. If number of owners decreased, the car would have a higher value price and it would be an overall, good car to buy on the market.

PROBLEMS

The problems with the data is:

1. It was incomplete
2. There were more of some makes than others.
3. The Age of a Car – There were certain cars that were expensive and I found a anonymous result, causing the prices to be pushed up; which was mentioned in the graph analysis of that topic.

CONCLUSION

In my overall conclusion, I have found out through this investigation that, there are several main factors that affect the price of a second hand car are; the age of the car, how many owners a car has and the price depreciation from when new.

In which, has proven my hypothesis to be true.

However, These factors are more important and have a greater affect on the second hand price than others, this is because, they show the consumer what to look for when buying a car.

These factors change the value of the car’s second hand price.

I found that how many owners, the price depreciation and the age of the car were strong influences, but I think that the mileage and the make of the car were not as strong, as they were shown to be weaker influences on the price of a second hand car.

If I were to improve the investigation, I would take a sample of 20 cars from each make and same colour. I would then take samples of 100 cars, but keep all but 1 variable constant and see the effect.

GCSE Mathematics Statistical Coursework

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