What factors influence the price of a second hand car

What factors influence the price of a second hand car?

There are many factors that will influence the buyer when purchasing a second hand car; age, model, make, colour, style, fuel, mot and condition to name a few.

I think that the age, mileage and engine size of the car will influence the buyer more than any other factor. My reasons are:

Age: I think age will be a major factor because older cars are generally not as popular as their newer counter parts, and an older car will probably have more problems than a younger model.
Mileage: I think mileage will be a major factor because a high mileage means a car has been driven a lot making the engine less efficient and may mean the car will be high maintenance.
Engine size: I think the larger the engine size the higher the price of the second hand car because a big engine size means the car will go faster which is quite important to most people.

To find out whether my hypotheses are correct I will need to collect some data. I have been provided with a data base of 100 cars. I will not use all 100 cars as this is too much data for me to work with. Instead I will take a sample of 40 cars as this will be an easier and fair amount to work with. To decide which cars to include in my sample I will first put the makes of the cars into a frequency table:

Out of the 100 makes the most information available is for Ford, Vauxhall, Rover and Fiat. It would thus be sensible that my sample is made up of these cars since if I take a sample from all 100 cars and end up with 5 Ford, 1 BMW, 1 Bentley and so on then it wont be a fair comparison since not all makes have the same value. Some cars are more exclusive then others. By looking at the 4 main makes in the database I can come up with realistic conclusion about certain makes.

Since I have decided on a sample size of 40 cars I have to decide how I am going to fairly select the data. Taking 10 cars of each make seems fair but there are only 10 Fiats so they will all have to be taken and so no selection has taken place. To make things fair and taking into account the proportion of each make I will take a stratified sample:

The sum of the four makes is 51

My sample size is 40

Ford = 16/51 x 40 = 12.54902 = 13 cars

...

This is a preview of the whole essay

The sum of the four makes is 51

My sample size is 40

Ford = 16/51 x 40 = 12.54902 = 13 cars

Vauxhall = 13/51 x 40 = 10.19608 = 10 cars

Rover = 12/51 x 40 = 9.411765 = 9 cars

Fiat = 10/51 x 40 = 7.843137 = 8 cars

So now I know how many of each make will be in my sample I will randomly select the cars by using the RAN# button on my calculator. I will number the Fords from 1 to 16 and then using my RAN# button I will get a random number and multiply it by 16 to find out which value to take. I will repeat this until I have my 13 cars. I will do the same process for the other makes. These are the cars that have ended up in my sample:

[PUT IN TABLE OF SAMPLE WITH RELEVANT SELECTED DATA]

In the table above I have a column with the second hand price, but I do not feel this is the best way to compare how much the car has gone down in value compared to other cars. For example: if we compare these two cars

Here put in an example to show why you would prefer using percentage depreciation. Also include how you will work out the percentage depreciation.

Now that I have all my data sorted I can begin to analyse it. I will begin by looking at the age of a car and what influence it has on the second price of a car.

I have drawn scatter diagrams of age vs. percentage depreciation for each make.

To find out whether I am right I need to first collect some data on cars. I have been provided with a sample of 100 cars from which I will select a sample of 50 cars to do my work for age and mileage. The reason being 100 cars is too much data for me to work with and 50 cars is a fair amount and should give me reliable results. I will take a random sample from the 100 cars so as to avoid any bias in my selection. I will do this by using the RAN button on my calculator.

e.g. I will ‘fix’ my calculator to give the random number to 2 d.p, I will then multiply this by 100 and this will give me the number of car that I should select.

When I am doing my work for make I will need to consider what makes there are in the data given so I will put the data into a frequency table. I will describe my plan for the make of the car later as I will be doing this after the age and mileage.

Once I have my data I will work out the percentage depreciation for each car as this is a much better measure of how much the car has gone down in value. For example…

To work out the percentage depreciation I will use this formula in an Excel spread sheet:

% depreciation = new price – second hand price x 100

new price

I will then draw a scatter diagram for % depreciation vs. age and % depreciation vs. mileage. I will comment on anything I find.

My sample of cars:

Some of the cars had data missing so I had to eliminate them altogether as they would not be useful for my research.

My first scatter diagram is age vs. % depreciation:

I have added the line of best fit to my graph. This shows me there is positive correlation between age and depreciation, that is, as the age increases so does the depreciation and this it what I expected. On further inspection I can see there are a few values that are far from the line of best fit.

[You should try and explain why you think these may be, and also why has the equation of the line of best fit been put in? describe how this can be used].

The scatter diagram also shows me that the depreciation varies a lot for an age, e.g. for a car 6 years old there are about 8 different % depreciation values and the same % depreciation value holds for cars 3,4,5,6 and 7 years old. So I do not think the scatter diagram is the best way to find out if age truly affects the depreciation of a car. I will instead work out the average percentage depreciation rate for different ages and see if there is a trend in this.

I have made a table of the results, and to work out the averages I took 2 cars for each age (1 – 10 years) as I had the data for this in my 50 cars:

The results clearly show that the trend is an upward one, that is, as the age increases the % depreciation generally increases. I have also shown this on the graph below:

I have so far only considered the age of the car irrespective of the make