Coefficient of Variation

A scale-free dispersion metric useful when comparing variability across series with different units or means.

CV % = σ ÷ μ × 100 (or sample s ÷ x̄ × 100).

Tip: Keep “Standard Deviation” and “Mean” on the same basis (period, units, and population) before calculating Coefficient of Variation.

Cluster: Statistics hub · Percentage error · Percentage guide

The coefficient of variation (CV) expresses spread relative to the mean as a percent.

Enter standard deviation and mean (same units). Mean must be non-zero.

σ or sample s
Mean of the data

Coefficient of Variation

Understanding Coefficient of Variation

How we calculate. CV % = σ ÷ μ × 100 (or sample s ÷ x̄ × 100). The form uses the same arithmetic as the worked examples on this page. See our methodology and accuracy policy.

Real-world scenario: A typical Coefficient of Variation case uses standard deviation 12 and mean 80. Enter the same figures below to reproduce the worked path.

What is Coefficient of Variation?

A scale-free dispersion metric useful when comparing variability across series with different units or means.

  • Same units for SD and mean
  • Mean ≠ 0
  • Higher CV = more relative variability

The Formula

Coefficient of Variation
CV % = (Standard deviation ÷ Mean) × 100

Worked Example

Scenario: SD = 12, mean = 80.
Step 1: 12 ÷ 80 = 0.15
Step 2: × 100 = 15%
Answer: Coefficient of variation is 15%.

Common Use Cases

  • Lab QA: assay variability
  • Process control: relative spread
  • Finance risk: return volatility vs mean

Pro Tips

  • Prefer CV when means differ
  • Watch signed means near zero
  • State sample vs population SD

Limitations: Coefficient of Variation results are educational statistics aids—not formal statistical certification. Confirm assumptions (SRS, large-sample approximations, labeling) for your analysis.

FAQ

Sample or population SD?

Either—use the same definition your study reports. The formula structure is identical.

What if mean is 0?

CV is undefined—relative variation needs a non-zero mean.

Authoritative References

For statistical definitions and survey practice, consult:

  • NIST ITL — measurement and statistical guidance
  • AAPOR — survey response-rate standards
  • NCHS — public health statistics context