# Coefficient of Variation Calculator

## How To Use Coefficient of Variation Calculator

Lets first understand, what is Coefficient of Variation (CV) and how we can calculate Coefficient of Variation?

In probability theory and statistics, the coefficient of variation (CV) is a standardized measure of dispersion of a probability distribution or frequency distribution.

It is often expressed as a percentage, and is defined as the ratio of the standard deviation $$\sigma$$ to the mean $$\mu$$.

Coefficient of Variation Calculation:

Let the set of n terms be x1, x2, x3, x4, x5, ......, xn.

$$Mean(\mu) = \frac{1}{n}\sum_{i=1}^n x_i$$ $$\mu= \frac{1}{n}(x_1 + x_2 + x_3 + ... + x_n)$$ $$\sigma = \sqrt{\frac{1}{n}\sum_{i=1}^n (x_i\hspace{0.1cm}-\hspace{0.1cm}\mu)^2}$$ $$Coefficient\hspace{0.1cm}of\hspace{0.1cm}Variation = \frac{\sigma}{\mu}$$

The coefficient of variation is useful because the standard deviation of data must always be understood in the context of the mean of the data. In contrast, the actual value of the CV is independent of the unit in which the measurement has been taken, so it is a dimensionless number.

For comparison between data sets with different units or widely different means, one should use the coefficient of variation instead of the standard deviation.

CVs are not an ideal index of the certainty of measurement when the number of replicates varies across samples because Coefficient of Variation is invariant to the number of replicates while the certainty of the mean improves with increasing replicates.

For Coefficient of Variation calculation using above calculator, you have to just write the comma separated values in the given input box and press the calculate button, you will get the result.