# Coefficient of variation calculator with steps (Sample, Population and Grouped)

## Coefficient of variation calculator

Example 1 Example 2

The online Coefficient of Variation calculator is a useful tool to easily calculate the variability of a given data set, including samples, populations, or grouped data. This calculator is especially helpful for statistics students as it provides step-by-step explanations for each calculation. The solution has three parts: the first calculates the mean, the second explains the standard deviation calculation in detail, and the last part shows the process to obtain the Coefficient of Variation.

To use the Coefficient of Variation calculator, follow these steps:

Step 1: Select the type of data you will be working with from the dropdown menu above the “Calculate” button. You can choose from population, sample, or grouped data.

Step 2: Enter your data. If you selected population or sample in Step 1, enter your data separated by commas in the yellow input box. If you selected grouped data, the interface will change and you will see fields to enter the class intervals and their respective frequencies.

Step 3: Once you have entered your data, click the “Calculate” button. A new box will appear with the solution explained step by step.

## What is coefficient of variation?

The coefficient of variation, also known by the term relative dispersion, is a statistical measure used to assess the variability of a data set in relation to its standard deviation.

Formally, the coefficient of variation is defined as the relationship between the standard deviation and the arithmetic mean of a distribution expressed as a percentage. It is commonly represented with the letters CV.

The formula for calculating the coefficient of variation is:

CV = (standard deviation / mean) x 100%

## How to find coefficient of variation

To calculate this coefficient you need to perform the following steps:

1. Find the arithmetic mean of the data set
2. Calculate the standard deviation
3. Apply the coefficient of variation formula, which consists of dividing the standard deviation by the arithmetic mean and all of this multiplied by 100.

When you use our calculator you will be able to see step by step the procedure to find CV.

## Coefficient of variation interpretation

The CV is used to determine the consistency of the data. When we talk about consistency we refer to the uniformity in the data values. Therefore, when comparing two data sets, the one with the lowest CV will be the one with the highest consistency.

In finance, the coefficient of variation allows investors to estimate volatility compared to the expected return on investment.

It is also often used to compare results of different tests or surveys. For example, if we assume that the CV of two surveys, A and B, is 3% and 8%, respectively, we could say that the data from Survey B are less consistent than those from Survey A, given its higher level of variability.

So, we can say that the smaller the CV value, or the smaller the ratio of the standard deviation to the mean, the better it is. A lower ratio suggests a higher tradeoff between risk and return.

## Solved examples

Example 01:  Find the sample coefficient of variance of the given data set (12.3, 22.5, 35.8, 44.8)

$\overline{x}=\frac{\sum x}{n}=\frac{115.39999999999999}{4}=28.85$
 $x$ $x-\overline{x}$ $\left(x-\overline{x}{\right)}^{2}$ $12.3$ $-16.55$ $273.9$ $22.5$ $-6.35$ $40.32$ $35.8$ $6.95$ $48.3$ $44.8$ $15.95$ $254.4$ $\mathrm{\Sigma }$ $0$ $616.93$
${s}^{2}=\frac{\sum \left(x-\overline{x}{\right)}^{2}}{n-1}=\frac{616.93}{4-1}=205.64$ $s=\sqrt{{s}^{2}}=\sqrt{205.64}=\overline{)14.34}$

$\begin{array}{rl}\text{CV}& =\left(\frac{s}{\overline{x}}×100\right)\mathrm{%}\\ \\ \text{CV}& =\left(\frac{14.34}{28.85}×100\right)\mathrm{%}=\overline{)49.71\mathrm{%}}\end{array}$