Sampling and Statistical Inference
Running head: DOMESTIC AND FOREIGN CAR SALES DATA ANALYSIS REPORT 1
DOMESTIC AND FOREIGN CAR SALES DATA ANALYSIS REPORT 2
Domestic and Foreign Car Sales Data Analysis Report
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Domestic and Foreign Car Sales Data Analysis
Introduction
The measurement of central tendency of data in statistics is important in helping a person make the right decisions when he or she wants to venture into business. The values obtained from measuring the central tendency are important in giving meaning to statistic figures (Sullivan & Verhoosel, 2013). The central tendency can be calculated in statistics using the mean, the median, and the mode (Kubiszyn & Borich, 2015). The standard deviation range is a good indicator that will help one to determine how data deviates from the mean (Mardia, 2014). The z-scores and the confidence levels also play a role in determining the deviation of various data from the mean, and they aid in figuring out the range through which he or she can get the true mean (Benjamin & Cornell,2014).
Summary of the Descriptive Statistics for Domestic and Foreign Car Sales
The mean was calculated using the AVERAGE function of excel for both domestic and foreign cars. The mean of the list price for the domestic car sales is 32.1625k and the sale price mean is 29.743. The mean of days to sell domestic cars is 32.905. For international car sales, the list price mean is 48.6555, the sale price is 46.207, and the average number of days to sell is 35.14. These values of the mean will give information on the average list price of car sales both domestically and internationally. The same applies to the sale prices and the days to sell for both domestic and international sales. The median gives the middle price of the list price, sale price, and the middle day to sell based on the data given. Looking at the foreign data, the middle list price is 50.05k, and that of the sale price is 48.85k. The middle day to sell is computed as 34. The median for domestic cars for the domestic list price is 25.55k, and that of the sales price is 27.55k. The median of the domestic days to sell is 31. In excel, the median is calculated using the MEDIAN function of excel.
The range is the difference between the maximum and minimum value of a given data. For the domestic list price, the maximum list price is 78.8k, and the minimum list price is 3.8k. Therefore, the range is 75k. When looking at the sale price, the maximum for domestic is 76.5k, and the minimum is 1.9k. Therefore, the range for the sale price of domestic cars is 74.6k. The maximum of days to sell is 70, and the minimum is 1. This makes the range to be 69. Looking at the coefficient of variation, it is the measure of variability of scores. It is calculated by dividing the standard deviation of a population with its mean, and the result is multiplied by 100. The coefficient of variation is used to make comparisons of two different data sets from different surveys that have different values. From the data for domestic sales, the coefficient of variation for the list price is 56. 93% and that of the sale price is 61.36%. The coefficients of variation for the days to sell is 54.29%. By comparing the coefficients of the three variables to the mean and standard deviation, the list price and the days to sell are closer to the mean of the list price and days to sell respectively than their standard deviations. For that of the sale price, the coefficient is closer to the mean as well. The same can be said about the coefficients of foreign sales. The coefficients of the list price, sale price and days to sell are 52.32%, 55.08%, 54.52% respectively for foreign sales.
When talking about the z-score, it is the number of standard deviations from the mean a data has. These can be achieved by standardizing the given data in excel. Using a technical language, z-scores can be defined as the number of standard deviations below or above the mean. For one to calculate the z-score, it is important that he or she knows the mean and the standard deviation of the data. The Z-score can be -3 or +3 in range. Any value above 2.5 can be used to standardize the scores. For this particular data, the range used is +3 to -3. The z-score is an important tool in statistics that helps one to easily find the outliers. An outlier can be said to be an observation point that deviates or does not resemble the other observations. That means that the observation would be very distant from the normal observation or a majority of observations. Form both the domestic and foreign data, there is only one outlier found in the days to sell foreign cars. From the data given, is marked in red. This outlier might have been found as a result of variability in the measurement, or it might be an experimental error.
The data for the above summary is shown in Table 1 and 2 below. Table 1 Domestic Car Sales.
Table 2. Foreign Car Sales.
Comparison of Results of Domestic and Foreign Car Sales
The average list price for domestic car sales is less than that of foreign car sales. And the same applies to the sales price. This might be because when conducting foreign business, there are more expenses incurred in the transportation of the cars and more taxes imposed by governments. Looking at days to sell, they are almost the same with a difference of two or three days. Days to sell have no effect on the list price and sales price of the cars because they are natural occurrences. Since the mean is different for both the domestic and foreign car sales, the standard deviations are expected to be different as well, and the same applies to the median and range.
Confidence Interval and Margin Error for Domestic and Foreign Car
The margin of error for the domestic mean sales price and days to sell is 2.58 and 2.53 respectively while that of foreign car sales is 3.6 and days to sale is 2.7. The margin of error statistics expresses the amount of random sampling of the data given during the survey. If a margin of error is large, the confidence becomes less. The margin of error gives information on the range above or below the mean that the true mean lies. The confidence interval gives the degree of uncertainty that can be associated with the given data. The confidence interval for the mean sales and days to sale domestic cars is 3 and 2.96 respectively and that for the foreign mean sales and days to sell is 4.2 and 3.1 respectively. The confidence level for the margin of error and the confidence interval is 98%.
The mean number of days to sell domestic cars for the sale price is estimated between 29 to 35 days under the confidence level of 98% and margin error of 2.5 that is rounded up to 3 for the sake of calculating days. For the foreign cars, it would be between 32 days and 38 days. If both the list price for domestic and foreign cars is $ 30,000, the domestic cars will be sold at $32, 600 while the foreign car would be sold at $32,700 based on the number of days.
Conclusion
From the data, there is a high probability of selling a car within a six day interval. This could have determined to form a confidence interval of 98 %. Overall, the number of cars sold both domestically and internationally for one month would be around four cars for domestic and three cars for foreign. This can be construed to mean that there needs to be an increase in aggressive marketing so that more cars are sold because of the depreciation effect of the cars.
References
Benjamin, J. R., & Cornell, C. A. (2014). Probability, statistics, and decision for civil engineers. Courier Corporation.
Kubiszyn, T., & Borich, G. (2015). Educational testing and measurement. John Wiley & Sons Incorporated
Mardia, K. V. (2014). Statistics of directional data. Academic press.
Sullivan, M., & Verhoosel, J. C. M. (2013). Statistics: Informed decisions using data. New York: Pearson.
List price mean in k32.1615
sales price mean in k29.743
days to sell mean32.905
median of list of price in k29.55
median of the sale price in k27.55
median of days to sell31
standard deviation of list price in k18.31094
standard devation sale price in k18.25088
standard deviation of days to sell17.86735
coefficinet varaiation of list price in k56.93434
coefficinet varaiation of sale price in k61.36192
coefficinet varaiation of days of sell54.2998
range of the lsit price in k78.83.875
range of sale price in k76.51.974.6
range of days to sell70169
List price mean in k48.6555
sales price mean in k46.207
days to sell mean35.14
median of list of price in k50.05
median of the sale price in k48.85
median of days to sell34
standard deviation of list price in k25.4554
standard devation sale price in k25.45091
standard deviation of days to sell19.15843
coefficinet varaiation of list price in k52.31763
coefficinet varaiation of sale price in k55.0802
coefficinet varaiation of days of sell54.5203
range of the lsit price in k89.51.1
range of sale price in k880.8
range of days to sell1001