This paper will study the domestic sale of Australian brandy by winemakers for the period of September 1989 to June 2014. Australia Bureau of Statistics (par. 2) provides data on brandy sales collected every quarter. The following is a set of 100 raw data about brandy sales in Australia measured in thousand liters of alcohol.
We will write a custom Case Study on Wine and Brandy Shipments in Australia specifically for you
301 certified writers online
|Period||Brandy Sales||Period||Brandy Sales||Period||Brandy Sales||Period||Brandy Sales|
Source: Australia Bureau of Statistics (Tables 2).
- A set of 100 raw data of brandy sales is tabulated above.
- The frequency distribution and histogram of brandy sales for Australia are illustrated below.
- The histogram has a tail that stretches to the right hence can be classified as a distribution that is skewed to the right. This means that few sales were made within classes that had more liters. As an example, there were few sales in the class of 432-494 compared with the class of 60-122.
- The mean, median, and mode are displayed on the summary table of descriptive statistics below:
Mean = 202.81
median = 179
mode = 117
- Sample standard deviation and variance are also tabulated in descriptive statistics above.
Standard deviation = 101.3856
Sample variance = 10279.04
- Median is the most appropriate measure of central tendency for skewed distribution. This is supported by the fact that the distribution contains outliers, which tend to temper with the mean. A comparison of mean, median, and mode for positively skewed distribution shows that mean is the highest value among the three measures hence the outliers will have a great effect on the mean compared with the median. This is why the median is applied as a measure of central tendency. In the case of a normal distribution, the mean is used as a measure of central tendency given that it does not contain outliers.
- The coefficient of variation for the sample is obtained as follows:
coefficient of variation = σ/i = 101.3856/ 202.81 = 49.99
CV = 50
- Z-score for minimum value:
Z score of maximum value
- Ogive for the distribution and median
According to the Ogive curve drawn above, the median is 180.
Australia Bureau of Statistics. Shipments of Wine and Brandy in Australia by Australian Winemakers and Importers. Cat. No. 8504.0, ABS, Canberra, 2014. Austats. Web.