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

0.00%
Population CV

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