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• Level: GCSE
• Subject: Maths
• Word count: 2205

# Statistically analyse the data given to me regarding Gary's used car sales.

Extracts from this document...

Introduction

My task for this coursework is to statistically analyse the data given to me regarding Gary’s used car sales. I shall begin with looking at the data. The following data was given to me.

 No. Price Price when New Age Make Mileage Engine Size 1 £6,970 £11,600 3 Ford 24,000 1.6 2 £3,350 £7,100 7 Peugeot 85,000 1.1 3 £3,995 £13,800 6 Ford 52,000 2.0 4 £5,300 £16,300 6 Vauxhall 70,000 2.0 5 £6,500 £8,700 3 Fiat 24,000 1.2 6 £1,500 £8,700 9 Vauxhall 82,000 1.6 7 £995 £8,500 9 Ford 102,000 1.8 8 £3,000 £10,400 7 Vauxhall 63,000 1.7 9 £7,495 £9,770 1 Vauxhall 8,000 1.4 10 £850 £7,540 10 Ford 124,000 1.6 11 £5,595 £11,000 4 Ford 41,000 1.6 12 £4,995 £9,880 3 Ford 34,000 1.4 13 £5,595 £14,000 4 Ford 55,000 1.6 14 £4,995 £11,500 4 Rover 40,000 1.4 15 £2,600 £12,000 7 Rover 82,000 1.6 16 £1,000 £6,200 10 Peugeot 119,000 1.1 17 £750 £5,100 11 Peugeot 96,000 1.0 18 £1,350 £9,140 8 Ford 108,000 1.6 19 £2,950 £17,750 8 Ford 96,000 2.9 20 £3,250 £9,990 7 Vauxhall 86,000 1.6 21 £5,650 £11,150 3

Middle

65,000

1.4

The first question which occurred to me was, is there any correlation between the difference between the price when new and the age. I expected there to be a positive correlation if there was one, showing that as the age went up, the drop in price from when the car is new and when it is re-sold increases. Below is a table of the Price differences and the age.

 No. Price Difference Age No. Price Difference Age 1 £4,630 3 19 £14,800 8 2 £3,750 7 20 £6,740 7 3 £9,805 6 21 £5,500 3 4 £11,000 6 22 £2,700 2 5 £2,200 3 23 £1,900 1 6 £7,200 9 24 £2,500 1 7 £7,505 9 25 £10,300 5 8 £7,400 7 26 £2,800 1 9 £2,275 1 27 £3,700 5 10 £6,690 10 28 £13,000 4 11 £5,405 4 29 £2,305 2 12 £4,885 3 30 £4,350 4 13 £8,405 4 31 £4,000 2 14 £6,505 4 32 £4,800 4 15 £9,400 7 33 £1,900 1 16 £5,200 10 34 £2,700 1 17 £4,350 11 35 £7,300 3 18 £7,790 8 36 £6,300 7

If you look at graph #1, you will see that I was wrong. There was no correlation between the price difference and the age. After seeing this, I thought that if I found what percentage of the original price the price difference is I could plot that in a scatter diagram to find the correlation between the depreciation percentage and the age. I found the depreciation with the equation

D=100-((o-p)*100)

Where D= Depreciation, o= the original price and p= price when used

 No. Depreciation (%) Age No. Depreciation (%) Age 1 39.91 3 10 88.73 10 2 52.82 7 11 49.14 4 3 71.05 6 12 49.44 3 4 67.48 6 13 60.04 4 5 25.29 3 14 56.57 4 6 82.76 9 15 78.33 7 7 88.29 9 16 83.87 10 8 71.15 7 17 85.29 11 9 23.29 1 18 85.23 8

Conclusion

Of these 15 values,

¨      80% were outside the majority age,

¨      73% cars were outside the majority mileage,

¨      and 33% cars were outside the majority engine size.

One of the cars, car 25, was reliant on the engine size to make it an unusually priced car, having values for mileage and age close to the mean values for both. The size of the engine gave it an unusually high depreciation.

All the above data prove that the age and the mileage are the two most prominent deciding factors of the price and depreciation of a car, with the size of the engine entering into the equation if there is nothing out of the ordinary about the age and mileage.

In conclusion, I have discovered the following facts about the data provided:

·        I found that there is no correlation between the price difference and the age, using a scatter diagram.

·        I found that there is a strong positive correlation between the depreciation and the age, using another scatter diagram.

·        I found a way to predict a percentage loss using a line of best fit and the lines equation.

·        I found that a car decreases in value more in its first three years than at any other time using a scatter diagram.

·         I found the main contributing factors and one backup factor to the price using the standard deviation, mean, inter-quartile range and majority range for the prices.

This student written piece of work is one of many that can be found in our GCSE Gary's (and other) Car Sales section.

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