Coefficient of Variation (CV) Calculator

What is the Coefficient of Variation?

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 to the mean. The CV is particularly useful when comparing datasets with different units or widely different means.

Formula and Its Meaning

The formula for the Coefficient of Variation is:

\[CV = \frac{s}{\bar{x}} \times 100\%\]

Where:

• \(s\) is the standard deviation of the dataset
• \(\bar{x}\) is the mean of the dataset

The CV represents the ratio of the standard deviation to the mean, and it is often expressed as a percentage. A lower CV indicates that the data points tend to be close to the mean, while a higher CV indicates greater dispersion around the mean.

Calculation Steps

1. Calculate the mean (\(\bar{x}\)) of the dataset.
2. Calculate the standard deviation (\(s\)) 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 CV for the dataset: 5, 20, 40, 80, 100

1. Calculate the mean: \[\bar{x} = \frac{5 + 20 + 40 + 80 + 100}{5} = 49\]
2. Calculate the standard deviation: \[s = \sqrt{\frac{(5-49)^2 + (20-49)^2 + (40-49)^2 + (80-49)^2 + (100-49)^2}{5}} \approx 39.12\]
3. Calculate the CV: \[CV = \frac{39.12}{49} \times 100\% \approx 79.84\%\]

Visual Representation

This scatter plot represents the example dataset. The red dashed line indicates the mean (49), and the spread of points illustrates the coefficient of variation (79.84%).