# How to Calculate the Coefficient of Variation

The Coefficient of Variation (CV) is a statistical measure that compares the dispersion or spread of data points in a data set relative to their mean. In other words, it evaluates how much variation exists within a set of data points. CV is often used in finance, where it represents the risk-to-reward tradeoff for investments, and in other fields where comparing variability of different datasets is essential. This article will discuss how to calculate the coefficient of variance step by step.

**Step 1: Calculate the Mean**

The first step in calculating the coefficient of variation is to compute the mean (average) of your dataset. The mean is the sum of all observations divided by the number of observations.

Mean = (Sum of all data points) / (Number of data points)

**Step 2: Calculate Deviation of Each Data Point**

Next, determine the deviation of each data point from the mean. This can be done by subtracting the mean from each individual data point. The deviation represents how far away each data point is from the mean.

Deviation = (Data Point – Mean)

**Step 3: Calculate the Squared Deviation**

To eliminate any negative deviations, square each deviation value obtained from step two.

Squared Deviation = (Deviation)^2

**Step 4: Compute the Variance**

Calculate variance by finding the average of all squared deviations. This average represents how variable your dataset is compared to its mean.

Variance = (Sum of Squared Deviations) / (Number of data points)

**Step 5: Find the Standard Deviation**

The square root of variance represents what’s called standard deviation (SD). It helps to understand whether your dataset’s dispersion is small or large.

Standard Deviation = √(Variance)

**Step 6: Calculate Coefficient Of Variation**

Finally, divide standard deviation by your dataset’s mean and multiply by 100 to obtain the coefficient of variation (CV). It measures relative variability, which helps when comparing datasets with different units or scales.

Coefficient Of Variation (CV) = (Standard Deviation / Mean) * 100

**Conclusion**

The coefficient of variation is a useful measure in evaluating the relative dispersion of a dataset. It allows for the comparison of datasets with different scales or units, which can be particularly helpful in finance and other fields that require understanding variability. By following the above steps, you can effectively compute the coefficient of variation for your data set and make more informed decisions based on your findings.