Summary of data on the Gross Regional Product in yuan using measures of central tendency and dispersion (e.g., mean, median, variance and standard deviation) and discussion on the strengths and weaknesses of these measures from the perspective of a manager seeking to…
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This indicates that some of the provinces may be very poor while others may be very rich although we still have to validate this when the data are transformed into gross regional product per capita.
A standard deviation of 759,648.2 million yuan which is very close to the mean value of 892,031.93 million yuan. This indicates a very high variability. The high variability is also indicated by the high variance of 5,770,653,964 million yuan.
From the perspective of the manager, the mean as measure of central tendency is very useful. However, the mean can mask a situation in which some of the provinces or cases have actually very high or very low variable values. The mode can be almost useless for ratio data but is very useful for nominal data or variables. The median is extremely useful to identify at what value the population is divided into 2 equal parts: half below the median while the other half is above the median. For instance, in the data above, the median is 609,110 million yuan versus the mean value of 892,031.93 million yuan or that the median is lower than the mean. This indicates that a few provinces with high values of the gross regional product are raising the mean to be above the median.
Given a poverty figure, for example, we can determine through the median whether at least half of the population are below or above the poverty figure. Another option is to use a measure of living standard. A median above the living standard would indicate that at least half of the population are above the living standard.
For ratio data, it is the belief of this writer that the using both the median and the mean simultaneously would be useful. However, for nominal variables, the identification of central tendency through the mode will the one useful.
1.2. The Pearson correlation coefficient between the gross regional product and gross capital is positive 0.97408077 versus the perfect correlation of positive 1.
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