During scientific research, many are faced with the variability of the trait being studied for individual units of the population, its fluctuation relative to a certain value, that is, with its variation. Here it should be taken into account in order to obtain the most reliable information on the progress of a particular scientific research.
Most researchers, when determining the interval of change in the value of a parameter, most often resort to absolute and relative indicators. Among the latter, the coefficient of variation is most widely used, which, if the studied quantity is characterized by a normal distribution, is a criterion for the uniformity of the population. This indicator allows you to determine what degree of dispersion will have the values of the investigated parameter, not paying attention to the scale and unit of measurement.
The coefficient of variation can be calculated by dividing the standard deviation by the arithmetic mean of the variable, expressed as a percentage. The result of this calculation can fall in the range from zero to infinity, increasing with increasing variation of the trait. If the obtained value is less than 33.3%, the variation of the attribute is weak. If more - strong. In the latter case, the studied data set is heterogeneous, its average value is considered atypical, and therefore cannot be a general indicator. Therefore, for this population, it is worth using other indicators.
It is worth noting that the coefficient of variation not only characterizes the homogeneity of a certain population, but is also used as a comparative estimate of it. For example, it is used if it is necessary to compare the sizes of fluctuations of a particular attribute in aggregates for which the calculated average value is different. In this case, the scatter of the obtained data does not allow an objective assessment of the acquired value. The coefficient of variation characterizes the relative variability of the variable, and therefore can be a relative measure of the fluctuation of the value of the studied parameter.
However, there are some limitations. In particular, it is possible to evaluate the degree of fluctuation of the parameter values only for a specific attribute and if the population has a certain composition. Moreover, the equality of these indicators can indicate both strong and weak variations. This is the case if the signs are different or the studies are conducted on different sets. Such a result is formed under the influence of very objective reasons, and this should be taken into account during processing of the obtained experimental data.
The coefficient of variation is widely used in the statistical processing of data in various fields of science and technology. In particular, it is actively involved in assessing the fluctuation of parameters in economics and sociology. Moreover, the application of the coefficient becomes impossible if it is necessary to assess the variability of variables that are able to change their sign to the opposite. After all, then as a result of calculations incorrect values of this indicator will be obtained: either it will be very small, or it will have a negative sign. In the latter case, it is worth checking the correctness of the calculations.
Thus, we can say that the coefficient of variation is a parameter that allows you to evaluate the degree of variation and the relative variability of the average value. The use of this indicator allows you to identify the most significant factors, the emphasis on which will achieve the goals and solve the necessary tasks.