# coefficient of variation calculator

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## Coefficient of Variation calculator

Coefficient of Variation calculator can be used to calculate the coefficient of variation in the given data set by evaluating the ratio between standard deviation and mean of that set. After you insert your data set, it calculates the mean and standard deviation of data automatically in the background and delivers the very precise value for the coefficient of variation.

In this post, we will discuss the coefficient of variation, how to find coefficient of variation, CV formula, and how to use the coefficient of variation calculator.

## How to use our Coefficient of Variation Calculator?

To use the variation calculator, follow the below steps:

• Enter the values in the given input box and separate each value by using a comma.
• After entering the values, press the Calculate

The cv calculator will calculate mean, standard deviation, and coefficient of variation as soon as you hit the calculate button. It will give you step by step calculations, which makes it very convenient for a student to understand the whole process of coefficient if variation calculations.

## What is Coefficient of Variation?

The coefficient of variation is a normalized measure of the dispersion of a probability distribution in statistics and probability theory. It is calculated as the ratio of the standard deviation to the mean.

## Coefficient of Variation Formula

The formula for the coefficient of variation is given below:

$$c_v=\frac{\sigma }{\left|\mu \right|}$$

$$\sigma =\sqrt{\frac{1}{N}\sum _{i=1}^N\left(x_i-\mu \right)^2}$$

In the above equations:
cv represents the coefficient of variation
σ refers to the population standard deviation

μ refers to the mean of the population data set

N refers to the size of the population data set, and
$$x_1,....,x_N$$ is the population data set

## How to calculate Coefficient of Variation?

To find the coefficient of variation using the above formula, follow the below steps:

1. Calculate the mean of the given data set. You use our mean calculator for that purpose.
2. Calculate the standard deviation for the given data set. You can also use our standard deviation calculator to calculate SD.
3. After calculating the mean and SD of the data set, calculate coefficient of variation by dividing standard deviation and mean.

### Example:

We will use an example to understand how to calculate CV by using the above steps and formula. Suppose we have a sample data $$60.25, 62.38, 65.32, 61.41$$ and $$63.23$$ of a population. Let’s calculate the coefficient of variation for this data.

Step 1: Calculate the mean value of the data set in the first step.

Mean $$= \dfrac{(60.25+62.38+65.32+61.41+63.23)}{5}$$

$$= \dfrac{312.59}{5}$$

$$= 62.51$$

Step 2: Calculate the standard deviation for the same values by placing values in the above SD formula.

$$\sigma =\sqrt{\Big(\dfrac{1}{5-1}\Big)\times (60.25-62.51799)^2+(62.38-62.51799)^2+(65.32-62.51799)2+(61.41-62.51799)^2+(63.23-62.51799)^2)}$$

$$\sigma =\sqrt{\Big(\dfrac{1}{4}\Big)\times (-2.26799)^2+(-0.13798999)^2+(2.80201)^2+(-1.10799)^2+(0.71201)^2)}$$

$$= \sqrt{\dfrac{1}{4} \times (5.14377 + 0.01904 + 7.85126 + 1.22764 + 0.50695)}$$

$$= \sqrt{3.68716}$$

$$\sigma= 1.92$$

Step 3: Calculate the coefficient of variance after getting mean and SD.

$$CV = \dfrac{\text{Standard Deviation}\left(\sigma \right)}{\text{Mean}\left(\mu \right)}$$

$$= \dfrac{1.92}{62.51}$$

$$= 0.03071$$

## Applications of Coefficient of Variation

Below are the various uses and applications of the coefficient of variation:

### 1.    Precision

The coefficient of variation helps us to make an accurate comparison between the different data sets. If the data sets have the same population, the ideal method for calculating the variation should be the standard deviation. However, if the comparison is between two different data sets, a better picture is given in the CV.

### 2.    Repeatability

The coefficient of variation measurement is a statistical figure. It helps us find out the repeatability and not its validity within a data set. In a way, knowing the degree of association, and not its agreement is more useful. The Variance Coefficient has its value when calculating data repeatability without needing to think too much about its validity.

### 3.    Consistency of data

The coefficient of variation is a useful concept for understanding data consistency. Data consistency means a sense of regularity inside the values in the data collection. The variance coefficient tests how stable the various values of the sample are from the mean. Consistency in a data set will be greater if the CV is low and smaller if the CV is higher.

### 4.    Assessment of Risk

The CV is the optimal tool for risk measurement in businesses. Risk managers like to use this tool more than anything else because it provides a better indicator of risk assessment at all levels.

### 5.    Decision Making

If you learn how to measure the CV, it will be simple for you to select the right choices open to you. The coefficient of variation is helpful anytime a company wants to reduce its operations because of the high costs involved. Any of its workers will have to quit the organization. It allows us to determine which department will be facing the hard hit.

## FAQs

### What is a good coefficient of variation percentage?

If the value of the coefficient of variation is less than 10, it is perceived as very good values. CV between 10 and 20 is also good value, but if this value gets greater than 30, it is not acceptable.

### Can the coefficient of variation be greater than 1?

Yes. The coefficient of variation can be greater than 1. In this case, it is considered to be a high variance. If it is less than 1, it is considered as the low variance for the given data set.

### Is a low coefficient of variation good?

Yes, a low coefficient of variation is good because it depicts the more accurate value. The greater value of CV is considered as a higher rate of dispersion around mean value.

### What is considered a low coefficient of variation?

The coefficient of variation less 1 is considered a low coefficient of variation in stats and probability theory.

### What is considered a high coefficient of variation?

If the value of the coefficient of variation is more than 1, it is considered a high coefficient of variation among the data set.

### Why do we use coefficient of variation?

The most common usage of the CV is to test the technique accuracy. It is often used as a variation indicator where the standard deviation is proportional to the mean. It is also used as a way of measuring variation between measurements produced in various units.

### What is the importance of the coefficient of variation?

The coefficient of variation has great importance when it comes to the variation in a data set. The coefficient of variance is important because the normal standard deviation must also be interpreted in light of the mean value. The real value of the CV is not dependent on the unit in which measurements are taken in comparison. The coefficient of variance can be used instead of the SD for comparison between data sets of varying units.

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