A coefficient of variation calculator identifies the relative variability of a dataset by expressing the standard deviation as a percentage of the mean.
How to calculate the coefficient of variation:
The CV measures dispersion relative to the mean, making it useful for comparing variability across datasets with different units or scales. A lower CV indicates less relative variability.
Step-by-step method:
- List all values in the dataset
- Calculate the mean (average) of the values
- Calculate the standard deviation (population or sample)
- Divide the standard deviation by the mean
- Multiply by 100 to express the result as a percentage
Formula:
CV = (σ / μ) × 100%
For sample standard deviation:
CV = (s / x̄) × 100%
Where σ (or s) is the standard deviation and μ (or x̄) is the mean.
Examples
Example 1: Dataset {600, 470, 170, 430, 300}
- Mean = 1970 / 5 = 394
- Sample variance = [(206² + 76² + 224² + 36² + 94²)] / 4 = 27130 / 4 = 27130
- Sample std dev ≈ 164.7
- CV ≈ (164.7 / 394) × 100 ≈ 41.80%
Example 2: Dataset {10, 10, 10, 10, 10}
- Mean = 10
- Standard deviation = 0
- CV = 0.00% — no variability relative to the mean
Key features include:
- Input for up to 50 values
- Automatic calculation
- Toggle between population and sample standard deviation
- Displays mean, standard deviation, and CV together
- Result expressed as a percentage
- Flexible list management — add or remove values freely
- Support for decimals and negative numbers
- Dynamic recalculation on every change