Coefficient of Variation Calculator
Calculate CV to measure relative variability and compare datasets with different means
Calculate Coefficient of Variation
Average value of the dataset
Measure of data spread around the mean
Coefficient of Variation Results
Mean: 0.000
Standard Deviation: 0.000
Formula: CV = (σ/μ) × 100%
Example Calculation
Quality Control Example
Scenario: Manufacturing process producing bolts
Sample data: Bolt lengths (mm): 50.2, 49.8, 50.1, 49.9, 50.0, 50.3, 49.7
Sample size (n): 7
Sample mean (x̅): 50.0 mm
Sample standard deviation (s): 0.21 mm
Calculation Steps
1. Calculate sample CV: CV = (0.21/50.0) × 100% = 0.42%
2. Apply bias correction: Ĉᵥ = (1 + 1/(4×7)) × 0.42% = 1.036 × 0.42% = 0.43%
Result: CV = 0.43% (very low variability - excellent quality control)
CV Interpretation Guide
Low (< 10%)
Excellent precision
Ideal for quality control
Moderate (10-20%)
Acceptable variability
Common in many applications
High (20-30%)
Significant variation
May need investigation
Very High (> 30%)
Poor precision
Consider data quality
Common Applications
Quality assurance and control
Analytical method precision
Investment risk assessment
Comparing dataset variability
Process monitoring
Important Limitations
Don't use with interval scales (temperature, dates)
Avoid when data contains positive and negative values
Undefined when mean equals zero
Can be misleading with means close to zero
Understanding Coefficient of Variation
What is Coefficient of Variation?
The coefficient of variation (CV) is a statistical measure that expresses the ratio of the standard deviation to the mean as a percentage. It provides a standardized measure of dispersion that allows comparison of variability between datasets with different units or scales.
Key Advantages
- •Unit-less measure enables comparison across different scales
- •Relative measure shows variability proportional to the mean
- •Widely used in quality control and risk assessment
- •Helps identify process consistency and reliability
Formulas
Population CV
CV = (σ/μ) × 100%
Where σ is population standard deviation and μ is population mean
Sample CV
CV = (s/x̅) × 100%
Where s is sample standard deviation and x̅ is sample mean
Unbiased Sample CV
Ĉᵥ = (1 + 1/4n) × CV
Bias correction for small sample sizes, where n is sample size
Practical Applications
Manufacturing
Monitor process consistency and product quality
Finance
Assess investment risk relative to expected returns
Analytics
Evaluate measurement method precision and accuracy
Research
Compare variability between experimental groups
Interpretation Guidelines
CV < 10%: Low variability indicates excellent precision and consistency
CV 10-20%: Moderate variability, acceptable for most practical applications
CV 20-30%: High variability may indicate process issues or measurement errors
CV > 30%: Very high variability suggests poor precision or data quality issues