LaTeX
CV=\frac{s}{\bar{x}}\times100\%Variables
- CV: coefficient of variation
- s: sample standard deviation
- x̄: sample mean
How to use this formula
Expresses sample standard deviation relative to the sample mean.
Important notes
- It is unstable when the mean is near zero.
- Use only when a ratio scale and meaningful zero are appropriate.
Quick example
If x̄=50 and s=5, CV=10%.
Applicability, worked calculation, and verification
Assumptions and domain checks
- It is unstable when the mean is near zero.
- For the Coefficient of Variation, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- For the Coefficient of Variation, identify whether each quantity is a sample statistic, population parameter, estimator, or model value, and check the method assumptions.
Worked example
If x̄=50 and s=5, CV=10%.
Common mistakes
- When copying Coefficient of Variation, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- For the Coefficient of Variation, do not interpret a descriptive statistic as a causal or population conclusion without the sampling and model assumptions.
Continue the workflow
Use Coefficient of Variation in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
CV=\frac{s}{\bar{x}}\times100\%. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Introductory Statistics 2eOpenStax, Rice University — Reviewed probability and statistics definitions, notation, and formulas.
Frequently asked questions
What is the Coefficient of Variation used for?
Expresses sample standard deviation relative to the sample mean.
Can I copy this formula as LaTeX?
Yes. Copy CV=\frac{s}{\bar{x}}\times100\% or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.