Coefficient of Variation (CV) expresses standard deviation as a percentage of the mean. It’s dimensionless, making it useful for comparing variability across datasets with different scales or units.

Formula

CV = (s / x̄) × 100%

where:
s = sample standard deviation
x̄ = sample mean

Purpose

CV answers: “How much variability is there relative to the mean?”

Example

Dataset 1: Mean = 100, SD = 10 CV = (10 / 100) × 100% = 10%

Dataset 2: Mean = 1000, SD = 50 CV = (50 / 1000) × 100% = 5%

Interpretation: Dataset 1 is more variable relative to its mean, despite having smaller absolute SD.

Interpretation Scale

  • CV < 15%: Low variability
  • CV 15-30%: Moderate variability
  • CV > 30%: High variability

When to Use CV

✅ Ideal for:

  • Comparing variability across different scales
  • Financial data (comparing investment consistency)
  • Quality control (comparing processes with different target values)
  • Biological measurements (comparing within and between species)

❌ Not appropriate for:

  • Data with mean near zero
  • Negative values
  • Parametric statistical tests