Relative Dispersion Coefficient of Variation

Relative dispersion is the degree by which a value in a data set deviates from the mean. It is a dimensionless quantity that signifies the variance of data points from the mean.

Coefficient of variation is one of the commonest ways of calculating the relative dispersion. It is the ratio of the standard deviation to the mean multiplied by 100 to make a percentage. The value can be used to compare various data sets and their variance.

First, we must understand what dispersion is and how it is calculated before we can get into the specifics of relative dispersion calculations. After that, we can discuss the meanings of relative and absolute dispersion in more detail. Following that, we’ll talk about what the coefficient of variation actually is.

In order to gain a thorough understanding of this topic, students must first perform a step-by-step calculation to determine the coefficient of variation. Let’s start.

Why Do We Need Dispersion?

It should be noted that averages do not provide a sufficient representation of any data set. We can only infer the mean or average value from them; we have no way of knowing how wide the range of values is between those values. For instance, consider the following data sets.

Even though they all have an average of 15,000 points, the dispersion of Set C is significantly greater than the dispersion of the other two sets of points In Set C, the data points are extremely dispersed in relation to the mean value.

So, what is this dispersion? Let’s find out.

What is Dispersion?

The amount by which the values of a data set are spread away from the average value or the mean value is indicated by the term dispersion. It provides a measure of the extent to which the mean and the other points in the data set differ from one another. There are four approaches that can be used to accurately measure dispersion or the degree of variance. They are –

• Range

• Quartile Deviation

• Mean Deviation

• Standard Deviation

These are also referred to as absolute measures of dispersion in some circles. It is possible that these measures of dispersion will be difficult to interpret at times in the future. They may provide inaccurate results, and they may be ambiguous in their communication of the information they wish to communicate.

Hence, we use relative measures of dispersion of which coefficient of variation is one.

Every absolute measure of dispersion has a corresponding relative measure of dispersion. The relative measures of dispersion are –

• Coefficient of Range

• Coefficient of Quartile Deviation

• Coefficient of Mean Deviation

• Coefficient of Variation (for standard deviation)

How to Calculate the Coefficient of Variation?

The coefficient of variation formula is as follows –

Coefficient of variance formula = (Standard Deviation)/Arithmetic Mean * 100

It is expressed as a percentage and is the most commonly used relative measure of dispersion.

To calculate the coefficient of variation we first have to calculate the standard deviation and the arithmetic mean, followed by the coefficient of variance formula.

How to calculate the standard deviation

Follow these steps and calculate the standard deviation –

Step 1: Calculate the arithmetic mean for all the values of the data set.

Step 2: Then calculate the difference between the data points and the arithmetic mean.

Step 3: Square these values.

Step 4: Add all these squared values.

Step 5: Divide the sum by the number of data points.

How to calculate Arithmetic Mean

Follow these steps and calculate the arithmetic mean –

Step 1: Sum up all the values in the data set.

Step 2: Divide the answer in Step 1 by the number of numbers.

Step 3: You should get the arithmetic mean.

How to calculate the coefficient of variation:

Finally, these are the steps to calculate the coefficient of variation –

Step 1: Divide the standard deviation by the arithmetic mean and you will find the coefficient of variation.

Step 2: Multiply the value into 100 and you will find the coefficient of variation as a percentage.

Conclusion

In conclusion, the coefficient of variation is the relative dispersion measure of the absolute standard deviation. It is also known as the coefficient of standard deviation. Dispersion is a way of understanding the spread of data. The coefficient of variation indicates the extent to which data in a sample differs from the mean of the population in relation to the mean of the sample. In finance, the coefficient of variation allows investors to determine how much volatility, or risk, they are willing to accept in relation to the amount of return they anticipate from their investments. The coefficient of variation (CV) is defined as the relationship between the standard deviation and the mean. The greater the level of dispersion around the mean, the greater the coefficient of variation. With a lower coefficient of variation, a more precise estimate can be obtained.