In order to prove or disprove my first hypothesis “I predict that the depreciation of a used car depends on its age.” I will be using the stratified selective sample that I have outlined above. The advantage of using a stratified sample is that it minimises the amount of bias in the sample.
The graph shows the effect age has on the percentage decrease in price of a car. The results show that age has a large effect on the prices of second hand cars. With an increase in age the decrease in price as a percentage also increases. For example the Mercedes AvantGarde has a percentage decrease in price of just 31.67% whereas the Fiat Tempra has a decrease of 87.58%. This is due to the fact that the Mercedes is only 2 years old and the Fiat is 6 years old. This is reflected in the graph by a very strong positive correlation between the data. This suggests that the older a car gets, the greater its percentage decrease.
The mean age is 5.72; this was calculated by adding the age values together and dividing by the size of the sample.
The modal age is 6 as this is the age value that occurs most often in the data, eight times in total.
The median age is 6.5 as this is the middle value when the data is arranged in order of size.
The spread of data is 10 as this is the number of different ages in the sample.
From the cumulative frequency graph I can predict the percentage of cars that are a certain age.
2-3 years old = 4-3 = 1/25 = 4% or 0.04 probability
3-4 years old = 6-4 = 2/25 = 8% or 0.08 probability
4-5 years old = 10-6 = 4/25 = 16% or 0.16 probability
5-6 years old =1 8-10 = 8/25 = 32% or 0.32 probability
6-7 years old = 21-18 = 3/25 = 12% or 0.12 probability
7-8 years old = 22-21 = 1/25 = 4% or 0.04 probability
8-9 years old = 24-22 = 2/25 = 8% or 0.08 probability
9-10 years old = 24-24 = 0/25 = 0% or 0 probability
10-11 years old = 25-24 = 1/25 = 4% or 0.04 probability
The probability shows that if a car was picked at random from the data the probability that it would be between 3-4 years old is 0.08 out of 1.
As the box and whisker diagram shows, the data has a wide spread of values. However it also has a small interquartile range, this tells us that much of the data is highly concentrated around the median.
From the above results I can conclude that my hypothesis was correct. The price of a used car is primarily based upon its age. This is because the numbers of new cars in production has increased rapidly in the last decade and older cars are now less desirable. The second hand car trade is suffering because of this.
However there are some limitations in the above data. The fact that the used price of a second hand car is not solely based on age causes a problem. For example a car that is 2 years old may depreciate faster than a car that is 3 years old. This may be due to the fact that the newer car has lower specifications such as no airbags, no air conditioning or no full MOT history. This will cause it to depreciate in value faster as it is less desirable. These variables may have affected my results.
In order to prove or disprove my second hypothesis “I predict that the price of a used Vauxhall is dependant on engine size.” I have selected all of the Vauxhall models from the data.
The table above shows all Vauxhall cars from the data sheet. I have selected only one type of car in order to minimize the effect of price brackets and effect of brand names. For example a Rolls Royce is much more expensive than a Vauxhall. This should reduce the chance of any anomaly occurring.
The graph above shows that with an increase in engine size there is also a slight increase in the percentage decrease of the car. This suggests that a car with a larger engine depreciates in value faster than a car with a smaller engine.
The mean engine size is (22/13) = 1.7 this is calculated by combining the engine sizes of the sample and dividing by the sample size.
The modal engine size is 1.5 as both 1.4 and 1.6 occur four times in the sample.
The median engine size is 1.65 as this is the middle value when the data is arranged in order of size.
The spread of data is 6 as there are 6 different engine sizes in the sample.
From the cumulative frequency graph I can predict the percentage of cars that have a certain engine size:
1.2-1.4 = 5-1 = 4/13 = 31% or 0.31 probability
1.4-1.6 = 9-5 = 4/13 = 31% or 0.31 probability
1.6-1.8 = 10-9 = 1/13 = 8% or 0.08 probability
1.8-2.0 = 11-10 = 1/13 = 8% or 0.08 probability
2.0-2.5 = 13-11 = 2/13 = 15% or 0.15 probability
From the Box and Whisker diagram we can see that the data has a wide spread of values. However unlike age it also has a large inter quartile range. This tells us that much of the data is widely spread around the median.
From the results above I can conclude that my hypothesis was incorrect. The price of a used Vauxhall may be based on its engine size. However as the engine size increases, so does the rate of the percentage decrease in price. This can be explained by the fact that as a car’s engine size increases it becomes less economical and more expensive to insure. Also as a car’s engine size increases the size of the car generally increases. The larger cars are often preferred by families and so tend to have high mileages. This may have had an adverse effect on my results, as both insurance group and mileage are variables in the data.
In order to prove or disprove my third hypothesis “I predict that the price of a used car is dependant on mileage.” I will be using the stratified random sample that was explained at the beginning of the investigation.
The graph shows the effect that mileage has on the percentage decrease of a price of a second hand car. The graph shows a very strong positive correlation. It shows that as mileage increases the percentage decrease in price of a second hand car also increases. This is shown by the fact that a Fiat Tempra with a mileage of 81000 has a percentage decrease in price of 87.58% and that a Mercedes AvantGarde with a mileage of 17000 has a percentage decrease in price of 31.67%. This data supports my theory that with an increase in the mileage of a second hand car there is also an increase in the percentage decrease of price for that car.
The mean mileage is 1169000/25 = 46760.
The modal mileage is 49000 as this occurs most often, five times in total.
The median mileage is 49500.
From the Box and Whisker diagram we can see that the data is very evenly spread. The inter quartile range is relatively small. This suggests that the data is tightly concentrated around the median.
From the above results I can conclude that my hypothesis was correct. The price of a second hand car depends on its mileage. As the mileage of a second hand car increases, the percentage decrease in price of the car also increases. This can be explained by the fact that as a car’s mileage increases so does its age. As already shown above, age has a large impact on the price of a second hand car. Also as a car’s mileage increases so does the wear and tear on the car. This can lead to expensive repairs and may affect the length of the MOT history.