Coefficient of Variation Calculator

How to Calculate the Coefficient of Variation

The Coefficient of Variation (CV) is a statistical measure of the relative variability of a dataset. It's particularly useful when comparing the degree of variation from one data series to another, even if the means are drastically different from each other.

Coefficient of Variation Formula

The formula for the Coefficient of Variation is:

\[ CV = \frac{\sigma}{\mu} \times 100\% \]

Where:

• CV is the Coefficient of Variation
• σ (sigma) is the standard deviation of the dataset
• μ (mu) is the mean of the dataset

Calculation Steps

1. Calculate the mean (μ) of the dataset
2. Calculate the standard deviation (σ) of the dataset
3. Divide the standard deviation by the mean
4. Multiply the result by 100 to express it as a percentage

Example Calculation

Let's calculate the Coefficient of Variation for the following dataset: 23, 45, 67, 89, 12, 34, 56, 78, 90, 11

1. Calculate the mean: \[ \mu = \frac{23 + 45 + 67 + 89 + 12 + 34 + 56 + 78 + 90 + 11}{10} = 50.5 \]
2. Calculate the standard deviation: \[ \sigma = \sqrt{\frac{\sum_{i=1}^{n} (x_i - \mu)^2}{n - 1}} \approx 30.39 \]
3. Calculate the Coefficient of Variation: \[ CV = \frac{30.39}{50.5} \times 100\% \approx 60.18\% \]

Therefore, the Coefficient of Variation for this dataset is approximately 60.18%.

Visual Representation

A visual representation can help understand the concept of Coefficient of Variation. Here's a diagram showing the distribution of a dataset with its mean and standard deviation:

This diagram illustrates a normal distribution. The red dashed line represents the mean (μ), while the green dashed lines show one standard deviation (σ) away from the mean on either side. The Coefficient of Variation expresses the standard deviation as a percentage of the mean, providing a standardized measure of dispersion.