How to calculate the coefficient of variation

The coefficient of variation is a statistical measure that allows to evaluate the dispersal of data in relation to the average. It is widely used in many areas, such as finance, economy and statistics, to compare the variability of different data sets.

What is the coefficient of variation?

The coefficient of variation, also known as CV, is a relative dispersion measure that expresses data variability in relation to the average. It is calculated by dividing the standard deviation by the average, multiplied by 100.

Mathematically, the coefficient of variation is represented by the formula:

cv = (standard/medium deviation) * 100

How to calculate the coefficient of variation step by step

To calculate the coefficient of variation, follow the following steps:

1. Calculate the average data;
2. Calculate the default data deviation;
3. Divide the standard deviation by the average;
4. multiplies the result by 100.

Let’s use an example to illustrate the calculation of the coefficient of variation:

In the example above, we have the following data: 10, 15, 20, 25 and 30.

Step 1: Calculate the average data:

Average = (10 + 15 + 20 + 25 + 30)/5 = 20

Step 2: Calculate the standard data deviation:

Standard deviation = √ (((10 20) ² + (15 20) ² + (20 20) ² + (25 20) ² + (30 20) ²) / 5) ≈ 7.07

Step 3: Divide the standard deviation by the average:

cv = (7.07/20) * 100 ≈ 35.35%

Therefore, the coefficient of variation for the data presented is approximately 35.35%.

Interpretation of the coefficient of variation

The coefficient of variation is a relative measure of dispersion, ie it allows comparing the variability of different data sets, regardless of the units of measurement used.

The higher the value of the coefficient of variation, the greater the dispersion of the data in relation to the average. On the other hand, the lower the value of the variation coefficient, the lower the dispersion of the data.

It is important to note that the coefficient of variation is only applicable to data sets that have a positive average. If the average is zero or negative, the coefficient of variation cannot be calculated.

Conclusion

The coefficient of variation is a statistical measure that allows to evaluate the dispersal of data in relation to the average. It is calculated by dividing the standard deviation by the average, multiplied by 100. The higher the value of the coefficient of variation, the greater the dispersion of the data in relation to the average.

It is important to use the coefficient of variation in conjunction with other statistical measures for a more complete data analysis. Moreover, it is essential to understand the interpretation of the coefficient of variation and its limitations.

I hope this article was useful for you to understand how to calculate the coefficient of variation. If you have any questions, leave it in the comments!