# Car Prices

By exponentially it means that a graph of a certain make of car, its price on one axis and its age on the other, would show a curved decrease in price over a period of time as shown in the example on the following page. The following experiment is being conducted to help and assist people who are buying and selling cars in magazines such as “Auto Trader”.

Approach Throughout the project I have referred to the second hand car sales pages in the magazines “Auto Trader” and “Exchange & Mart” (in the local paper) for data. In these, I found a wide range of data over three weeks from which to select the type of data required. I selected relevant pieces of data in each age range for the Mercedes C-Class. If there was not enough information in the source I would have referred to another car magazine. Due to the fact that sampling concentrates on gaining information about selected sampling units, the quality of information gained is better than if the information was of units that had not been specified. Ideally, it would have been best to use random sampling but as the data available was already limited, it was decided

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to take all the data available over a three-week period.

When choosing data, it is very important to select data to be included in testing on an unbiased selection process. This ensures that the results are reliable. If the data was biased in anyway this would mean that, although the hypothesis may seem to be true, it cannot be applied to other situations and may be of limited value. In this statistical work I only used one type/make of car, Mercedes, and within this I used only the “C-class” range and within that, the saloon style. By doing this it restricted the type of sample chosen and I also limited the price variation to a very small number of factors – i.e. number of doors, age. Other factors such as condition, mileage, modifications, etc. are still relevant but finding data and producing appropriate graphs would be too difficult. To validate the results further I conducted the same experiment with the Volkswagen Golf GTI Hatchback, limiting the range to five-door cars with a diesel engine sized between 1.8l and 2.2l, as well as the other factors mentioned before.

he results gathered from the standard deviation information show that the spread of all the plotted figures is fairly small. This is also the case for the fifth year in the Mercedes car data, which means that even though the results are out of line, the plotted data is close together within a small price range.

Analysis

As seen in the data table above, all the Mercedes C-Class cars that are five years old seem to be out of line compared to the expected pattern (they are highlighted in the table). The graph above shows these anomalous results. They could be due to one of the following: 1. Features which have been added to the car by previous owners. 2. There could have been a limited edition/selected batch of this type of car made that year. 3. Due to the rate of inflation, as all the cars that are five years old are priced higher than would be expected according to the trend. This is by far the most likely reason.

The exponential decrease of the Mercedes C-Class was discovered by examining this data. When anaIysing the data obtained, the average price drop after the initial year of sales was found to be from 500 (30%) compared to the original price. In the second year, the car price dropped by another 8,000 (a 35% decrease in value). Then, the rate of decrease, in terms of value, slows down, levelling out. This fits the theory of exponential devaluation indicated by the “line of best fit”.

One of the drawbacks in analysing the data was that the averages were taken for each year. This type of average, i.e. the mean, suffers from distortion based on single anomalous or outlying values. Under the circumstances a different type of average e.g. the median may have been more appropriate. One point to make here is that the mean price for the 5-year-old vehicles was obtained from four sample values. If this year’s average had been discounted from the plotted data, a much truer analysis would have been possible.

Therefore, when I marked in the exponential curve “line of best fit”, I discarded the anomalous result and drew the expected trend of devaluation for the car. Also, the average for the 4th year’s data is likely to be more accurate than the 8th year’s, because it is an average of 14 pieces of information whereas, for the 8th year, it is an average of only three pieces of data. In general, the greater the range of data, the more accurate the constructed picture can be.

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