Coefficient of Variation

In statistics, the two most essential metrics are variance and standard deviation. Standard deviation is a measure of the distribution of statistical data, whereas variance is a measure of how data points differ from the mean. The main dissimilarity among the two is that standard deviation is articulated in the same units as the data mean, whereas variance is expressed in squared units.

Dispersion measurement types:-

In statistics, there are two primary types of dispersion methods:

• Absolute Dispersion Measurement
• Dispersion Measurement in Relative Terms

Absolute dispersion measurement

The same unit as the original data set is used in an absolute measure of dispersion. The absolute dispersion approach expresses changes as the average of observed deviations, such as standard or mean deviations. It includes terms such as range, standard deviation, and quartile deviation, among others.

Relative measure of dispersion

When comparing the distribution of two or more data sets, relative measures of dispersion are used. This metric compares values without the use of units. The following are some examples of common relative dispersion methods:

1. Coefficient of Range
2. Coefficient of Variation
3. Coefficient of Standard Deviation
4. Coefficient of Quartile Deviation
5. Coefficient of Mean Deviation

Coefficient of variation:-

A form of a relative measure of dispersion is the coefficient of variation. It’s calculated as the standard deviation divided by the mean. The coefficient of variation is a dimensionless variable that is usually expressed as a proportion. It aids in the comparison of two data sets based on the degree of variance. For both a sample and a population, the coefficient of variation may be calculated. The coefficient of variation is used in areas like finance to assist investors analyse the risk-to-reward ratio.

Definition:-

The coefficient of variation, defined as the ratio of the standard deviation to the mean, is a dimensionless relative measure of dispersion. When there are many data sets with different units, the coefficient of variation is the most effective technique to compare them.

Examples: –

Assume you have a data collection of [80, 90, 100]. The population standard deviation is 8.165, while the mean is 90 and  0.09 is the coefficient of variation. The coefficient of variance is 9% in percentage terms.

Coefficient of variation: –

The coefficient of variation may be calculated using two different formulae. The sample coefficient of variation is identical like the population coefficient of variation. In statistics, population infers to the whole group being considered. To put it another way, the population infers to the whole data compilation. The sample is a segment of these inhabitants that has been selected at random. The sample is utilized to signify the study’s whole population. The sample mean and the population mean will always be equal. Because the standard deviation values differ, there are two coefficients of the variation formula.

1. Population Coefficient of Variation =(σ/μ) *100
2. Sample Coefficient of Variation= (s/μ)*100

Steps to find the variation:-

The coefficient of variation formula is especially important when we need to compare data from two distinct surveys with varying values. The coefficient of variation formula (CV), also identified as relative standard deviation (RSD) in statistics, is a normalised measure of a probability or frequency distribution’s dispersion. If the coefficient of variation is low, the data has less variability and is more stable. The following are the basic steps for scheming the coefficient of variation:

1. First, look for the sample set
2. Secondly, determine the mean and standard deviation
3. Next, in the coefficient of variation formula [ CV =σ/μ× 100, μ≠0,], plug in the values

Utilisation of coefficient of variation:-

When comparing two data sets with comparable values, the standard deviation can be employed. When comparing two datasets with different units, however, the coefficient of variation must be employed. The following are a few cases of coefficient of variation applications:

• When an investor wishes to invest in a certain ETF, he utilises the coefficient of variation to determine which one will provide the best risk-return trade-off
• The coefficient of variation may also be used to assess data consistency. A distribution with a lesser coefficient of variation (CV) is extra steady than one with a greater CV

Conclusion: –

Coefficient of variation is a method of understanding the variability of data in a given dataset. It gives the relative measure of dispersion. The coefficient of variation has found its importance in the finance industry and to assess the data consistency in a given dataset. The variability of data in a wide range of dataset can be well clarified using the concept of coefficient of variation.