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**Education Calculators** ▶ Coefficient Of Variation Calculator

The team of calculator-online provided a smart coefficient of variation calculator that helps to calculate the coefficient of variation for a given data values. The coefficient of variation calculator allows you to calculate coefficient of variation (CV, RSD) of continuous data or binomial (rate, proportion) data.

Well, give a read to this article to learn how to find variance of coefficient and even about this fastest tool.

Now, let’s start with some basics!

The (CV) indicate as a statistical measure of the dispersion of data points in a data series around the mean. According to probability theory and statistics, it is the ratio of the standard deviation to the mean, and also known as relative standard deviation (RSD). In other words, CV is the measure of relative variability.

According to Investments theory, the coefficient of variance assists in determining which investment is better.

As mentioned-above, CV is the ratio of the standard deviation to the mean, so:

**CV = σ/ μ**

Where;

CV = Coefficient of Variation

σ = Standard Deviation

μ = Mean

Formula to calculate Standard Deviation:

σ = √((∑▒〖(x- μ)^2 〗)/(n-1))

Formula to calculate Mean:

μ = (∑▒x)/n

The advanced variance calculator specifically designed to compute the coefficient of variation of a set of data. The calculator helps to find the No. of samples, Mean, Standard deviation, C.O.V & C.O.V % for the given data values. Sometimes, this online tool also referred to as a coefficient of variance calculator.

If you are going to enter summary data, then you ought to select a ‘summary data’ option. This coefficient of variation calculator with mean and standard deviation inputs shows you the accurate results for the summary data.

You have to select dataset type, choose whether your data represents a population or sample

You have to add the mean of the data set

You have to add the standard deviation of the data set

**Note**: When you select dataset type “sample”, then you also have to add sample (n) into the designated field of calculator

Once you added the above values, then this coefficient of variation calculator shows:

- No. of Samples
- Mean
- Standard Deviation
- C.O.V
- C.O.V %

If you are going to enter raw data, then you ought to select ‘raw data’ option

- First, select proportions option from the drop down menu
- Then, you have to choose dataset type, it can be either ‘population’ or ‘sample’
- Then, you have to add sample size (n) into the designated field
- Very next, you have to choose proportions data from the drop-down menu, it can either ‘ Proportion e.g. 0.05’ or ‘Rate as Percentage e.g. 5%’ or ‘Number of Events e.g. 10’
- Finally, you ought to enter the number of events into the designated field

- First, you ought to select means option from the drop-down menu
- Then, you have to select the dataset type, whether ‘population’ r ‘sample’
- Then, you have to add data set separated with a comma

Whether you make a calculation for data for proportions or means, the coefficient of variation calculator will shows:

- No. of Samples
- Mean
- Standard Deviation
- C.O.V
- C.O.V %

You just have to remember the above formulas while calculating coefficient of variation of the sample data.

- First of all, you have to calculate the mean of the data set
- Right after, you have to calculate the sample standard deviation for the data set
- Finally, you have to find the ratio of sample standard deviation to mean to get the CV of the data set

**Problem:**

Find the coefficient of variance for the samples 62.25, 60.36, 64.28, 61.24, and 66.24 of a population.

**Solution:**

First, calculate Mean:

Mean = (62.25 + 60.36 + 64.28 + 61.24 + 66.24)/5

= 314.37/5

=62.874

Second, calculate Standard Deviation:

SD = √( (1/(5 – 1)) * 〖(62.25- 62.874)〗^2 + 〖(60.36- 62.874)〗^2 + 〖(64.28- 62.874)〗^2 + 〖(61.24 – 62.874)〗^2 + 〖(66.24- 62.874)〗^2)

= √( (1/(4) * 〖(-0.624)〗^2 + 〖(-2.514)〗^2 + 〖(1.406)〗^2 + 〖(-1.634)〗^2 + 〖(3.366)〗^2)

= √ ( (1/(4) * (0.389376) + (6.320196) + (1.976836) + (2.669956) + (11.329956)

= √5.67158

SD = 2.38150

Finally, Calculate (CV):

CV = Standard Deviation/ Mean

Put the values into the coefficient of variation equation:

= 2.38150/62.874

CV = 0.037877

No doubt, the (CV) coeffcieint of variation is very similar to the relative standard deviation (RSD), but the only prominent difference between both that the coefficient of variance can be negative, while RSD is always positive.

The CV is the statistic that will tell you whether the mean is negative or positive:

- A positive mean results in a positive Cv
- A negative mean results in a negative Cv

However, the RSD or relative standard deviation will take into account when you see the mean ± standard deviation (e.g., 11 ± 2% cm).

σ is represented as the standard deviation for a population that is the same as ‘s’ for the sample. μ is said to be the mean for the population that is the same as x̅ in the sample. In simple words, to calculate CV, you just have to divide the standard deviation by the mean and multiply by 100.

**The coefficient of variance formula is:**

Cv = (s / x̅) * 100%

You can easily calculate CV% as the ratio of the standard deviation of the sample to the mean of the sample that represented as a percentage. All you need to add the values in your dataset and divide the result by the number of values to attain the sample mean.

Simply, the percentage of CV plot point refers to the subgroup sample standard deviation divided by the subgroup means, and multiplied by 100. In effect, the %CV is said to be the percentage of the mean represented by the standard deviation – a relative measure of variation.

Remember that standard deviation (SD) is very sensitive to extreme values (outliers) in the data. However, there are certain useful measures of dispersion that are related to the SD:

**Variance:** The variance is said to be as just the square of the SD. For the instance, the variance = 〖(14.42 )〗^2 = 207.36

**CV:** The (CV) is the standard deviation divided by the mean. For the instance, CV = 14.4/98.3 = 0.1465, or 14.65 percent.

The standard deviation or SD of an exponential distribution of data is equivalent to its mean that making its CV to equalize 1. According to optimistic studies, distributions with a CV to be less than 1 are indicated as a low-variance, and those with a CV higher than 1 indicated as high-variance.

The CV represents the ratio of the standard deviation to the mean, and it is a statistic that is very useful for comparing the degree of variation from one data series to another, even if the means are drastically varying from one another.

The coefficient of variation (CV) represents what percentage of the mean the standard deviation is. More specifically, the CV is something that indicates how large the standard deviation is in relation to the mean. If the CV is 0.45 (or 45%), this means that the size of the standard deviation is 45% that of the mean.

However, if the CV is 0.46 (or 46%), then it is said to be the standard deviation is 46% that of the mean.

The CV is said to be the ratio of the standard deviation to the mean. However, remember that the higher the coefficient of variation, the greater the level of dispersion around the mean.

The acceptable variance is said to be 60 percentage as it is explained in factor analysis for a construct to be valid, is said to be as 60 %.

The C.O.V indicates the ratio of the standard deviation (SD) to the mean, and it is said to be a useful statistic for comparing the degree of variation from one data series to another. Even, C.O.V is useful if the means are drastically different from one another.

Keep in mind; the relative variability calculation is typically used in analytical chemistry, engineering and physics, factory production quality assurance etc. Also, it is taken into account for economists and social studies for economic, organizational and financial models. So, use the above formulas and to get instant results you can use the above coefficient calculator.

From Wikipedia, the free encyclopedia – According to The Theory And Statistics, The Coefficient of Variation (CV)

By ADAM HAYES – Reviewed By PETER WESTFALL – Financial Analysis – What does the coefficient of variation tell you!

Institute for Digital Research & Education (Statistical Consulting) – FAQ: Situations and Definitions About THE COEFFICIENT OF VARIATION

MathisFun – Probability and Statistics – Standard Deviation and Variance – The Way to Find Variance