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It is of significance to study variations in data collection as it will assist in understanding varied concepts of the data collected. Variation helps in illustrating the degree to which the information is spread out through the provided data. Such therefore allows for better comprehension of the statistical materials provided. Variations study also provides a means to visualizing and understanding statistical data being considered, something the mean or median is not developed to do. Studying variations also assists in the determination of the average reliability of data collected by indicating how far an average is a representation of the whole figures.
Besides, it creates an avenue for statisticians to compare two or more distributions (Spatz, 2016).
The major differences among data variation measurement elements are based on their formulas to help calculate dispersion aspects. The range is the most common and easiest approach as it measures data variations by determining the differences between the highest and smallest data distribution values. Although, such can be misleading formulae, especially with extremely big or small values hence not a reliable way of measuring data variation.
Regarding the standard deviation, the approach measures how far data points are spread out where low standard deviation indicates values are close to the mean set, and when the standard deviation is high, the values are spread on a wider range. The box-and-whisker plot creates a visual representation of dispersion and the central tendency, thus depicting the variability of the data sets. Although these approaches differ in calculation and measurement of data variations, they have one major similarity, and that is the shared contribution towards the determination of value dispersion.
Average in statistics is inadequate by itself as it is simply an attempt to summarize various data sets using a single number. Such may not always be meaningful as it requires statistical cross-referencing to help in measuring data spread. The average on itself does not provide a mathematical explanation of how data is distributed about the mean (Brase &Brase, 2016).
One of the main significances of the Coefficient of Variation is the element of being unitless. It is an important statistical tool due to its practicality and simple algorithm usage (Ma, Yao & Fang, 2018). It also allows for the measurement of data points dispersion statistically in a data series about the mean. It also allows for the comprehension of the standard deviation of data within the determination of the mean of statistical information provided. The coefficient of variation provides a significant basis for comparison among data sets with varied units or different means. In addition to that, it assists in measuring the relative variability of data sets presented when the standard deviation and the mean are proportional to each other. Lastly, the coefficient of variation effectively allows for the evaluation of relative closeness of actual value predictions (Brase & Brase, 2016).
In statistics, the coefficient of variation having no units indicates that both the denominator and numerator in defining coefficient of variation have the same units. The results are an expression of standard deviation in the percentage form of the mean. Such indicates that the coefficient of variation can easily be compared to each other in ways other measurement components cannot be measured, such as root mean squared residuals and standard deviations. The main advantages of having no units include the provision of an opportunity for directly comparing the variability of two different data populations using the coefficient of variations. Thus, such creates a better analysis of the relative spread of various data sets (Brase & Brase, 2016).
Relative size is an important aspect in statistics, especially on data collection, as it provides an analysis of how samples used in fact collection are connected or dependent on each other. According to Merriam-Webster (n.d.), it is an essential element as it helps in the expression of specific quantities to the total magnitude that is the value of the amount measured. Thus expresses the mean of amounts included and provides a basis for comparison between two or more sets of data as provided.
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