Business Finance

What is the coefficient of variation and how to find it?

coefficient of variation

The coefficient of variation (CV) is a measurable statistic of data points’ dispersion around the mean in a data series. Even if the means are significantly different, the coefficient of variation is a useful statistic for analyzing the degree of variance between two data series. It indicates the ratio of a standard deviation is a measure.

Coefficient Of Variation Interpretation

  • Purpose 

The variances in an initial data set are calculated also using standard deviation and coefficient of variation. The coefficient of variation, on the other hand, calculates the ratio of the volatility of the mean of the data collection.

  • Where to Use 

The coefficient of variability is indeed a useful tool for comparing the variability of measurements taken in various units. When determining the error margin or instability in your data sets, however, measuring standard deviation might be useful.

What Is CV Calculation and How To Calculate Coefficient Of Variation?

We can calculate the coefficient of variation for the population as well as for the sample through the same formula written below. 

The coefficient of variation is calculated using the following formula:

Coefficient of Variation =    SD/Mean × 100

In other words, divide the standard deviation by both the average and multiply by 100 to get the actual value of variation. 

Coefficient Of Variation Example

Two multiple-choice exams with various settings are being compared by a researcher. An attribute test is given in the first test. Alternative alternatives are given to the test takers randomly while conducting the second test. The following are the findings of the two tests:

Regular TestRandomized Answers
Mean59.944.8
SD10.212.7

It’s difficult to compare the 2 test findings. Because the averages are also different, comparing standard deviations isn’t particularly useful. The formula CV=  SD/Average into 100 can be used to assist make sense of the data:

Regular TestRandomized Answers
Mean59.944.8
SD10.212.7
CV17.0328.35

You would believe that the tests had comparable findings based on standard deviations of 10.2 and 12.7. When the results are adjusted for the comparison of means, the results become more significant:    

The Regular examination of this variation was 17.03 while for randomized responses CV was equal to 28.35. This shows that variability between multiple measurements may also be compared using the coefficient of variation. You can also compare IQ results to the Woodcock-Johnson III Test of Cognitive Functions through the exact variation of the coefficient. 

Coefficient Of Variation Vs Standard Deviation

The SD is used to find a value that is being measured by how much it deviates from the average value. While the coefficient of variation is itself measured while dividing SD to Average value. When comparing the variance between two datasets, the analysis of variance is more commonly utilized. The differences are enlisted as,

  • The standard deviation and coefficient of variation are both used to calculate the range of values in a dataset.
  • The SD is a finding of how much a value varies or deviates from the average
  • The standard deviation to mean ratio is measured by the coefficient of variation.
  • When we wish to measure the dispersion of values inside a single dataset, the standard deviation is more commonly utilized.
  • When comparing the variance between two datasets, the coefficient of variation is more commonly utilized.

What is a Good Coefficient of Variation?

When an exponential distribution’s standard deviation equals its mean, the coefficient of variation equals one. Low-variance distributions (such as an Erlang distribution) were low-variance, whereas high-variance distributions (including a hyper-exponential distribution) are high-variance.

What Is A Good Coefficient Of Variation Percentage

CVs of 5% less than generally imply good technique performance, but CVs of 10% or more imply poor method performance. However, before passing judgment on a variation of coefficient, you should carefully examine the mean value. The CV could be high at very small doses and low at extremely high values.

How Do You Find The Variance And Coefficient Of Variation?

The variance is directly proportional to the square of something like the SD. The variance for such an IQ example is 14.42 = 207.36. The coefficient of variation (CV) is the ratio of SD and Average of given values. For example, in this the variation in the IQ case will be such; CV = 14.4/98.3 = 0.1465, or 14.65.

What Is Coefficient Of Variation In Statistics?

The standard deviation to mean ratio is called the coefficient of variation (CV) which is the base of the Statistics. The larger the dispersion around the mean, the greater the coefficient of variation. In most cases, it’s given as a percentage. The more exact the estimate, the smaller the coefficient of variation value.

Coefficient Of Variation Finance 

The coefficient of variation is a financial term that helps investors to assess how much volatility, and risk is taken about the projected return on investments.

Also Read: How Do You Calculate the Debt-to-Equity Ratio?

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