The coefficient of variation or coefficient of variation of Spearman is a measure applied in the science of statistics, which relates the standard deviation and the arithmetic mean of a data set defining the relative dispersion of the sample in study.
In simpler words, it is the average or desired variation of a data set, with respect to the arithmetic mean.
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In the set of different dispersion measures applied in statistics, these are found in the same units by which they are being measured, being dimensional. However, it does not solve possible problems that may arise.
When a comparison of situations with different units of measurement is to be studied, a dimensionless measure of variability is required. This measure is the coefficient of variation.
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Having stated the above, the coefficient of variation makes it possible to compare the variability of different samples or populations, since it eliminates the dimensionality of the two variables. 
In this article you will find:
How is the coefficient of variation calculated?
Spearman's coefficient of variation is usually denoted by the initials (C.V). and can be calculated as follows:
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CV equals the arithmetic mean / standard deviation.
Bearing in mind that said coefficient is the relationship that exists between the standard deviation of the sample and its mean.
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CV = x 100%
Where:
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- is the standard deviation
- x is the mean
This coefficient allows comparison between dispersions of different distributions, provided they are positive. The calculation is made for each of these distributions and the values obtained can be compared with each other.
The largest dispersion is that corresponding to the coefficient of variation value higher.
What is its usefulness?
This indicator allows:
- Establish a relationship between the size of the mean and the variability of the variable.
- Establish comparisons between different cases.
Its calculation ensures:
- It is said to be less than one or eight. In other cases it can be greater than 1 or equal to 1.
- It can be expressed in percentages.
- It is applied in fields of probability, such as renewal theory and queuing theory.
- It is said to be a comparative measure for two samples, where the coefficient of variation with the highest magnitude coincides with the sample with the highest relative variability.
- Eliminate possible distortions of the arithmetic means of two or more populations.
- To compare variability of a data set.
This measure as a type of performance tries to concentrate in a single figure, the performance of the planned investment and the risk incurred by the investment measured as a standard deviation of the performance.
The CV coefficient of variation is calculated as a standard deviation divided by the mean. The consideration is that the lower the CV, the lower the risk for each unit of performance, it is worth it. It should be noted that this measure is erroneously used as an instrument to make a comparison between investments alternatives.
In conclusion, whenever it is expected to refer to the correspondence between the variability of some variable and the size of the mean, the known coefficient of variation in the statistics.
