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Coefficient of Variation

General

Coefficient of Variation (Relative Standard Deviation)

A standardized measure of dispersion calculated as the standard deviation divided by the mean, expressed as a percentage, useful for comparing variability across datasets with different units or scales.

Definition

The coefficient of variation (CV) is a standardized measure of dispersion calculated by dividing the standard deviation of a dataset by its mean, then expressing the result as a percentage. Unlike raw Standard Deviation, which is expressed in the same units as the original data, the coefficient of variation is unitless โ€” making it possible to compare variability across datasets that use completely different units or have very different means. The Coefficient of Variation Calculator computes this ratio directly from a dataset or from a known mean and standard deviation.

CV is especially useful when comparing the relative consistency of two datasets that wouldn't be comparable using standard deviation alone. For example, comparing the variability of employee salaries (measured in thousands of dollars) against the variability of employee tenure (measured in years) using raw standard deviation would be meaningless, since the units and scales differ โ€” but converting both to CV puts them on the same relative footing.

In finance, CV is often used to compare the risk-adjusted consistency of different investments by dividing the standard deviation of returns by the expected return, giving a "risk per unit of return" figure that's comparable across asset classes with very different average returns.

Formula

CV = (ฯƒ รท ฮผ) ร— 100%

Where ฯƒ is the standard deviation and ฮผ is the mean of the dataset.

Worked Example

Consider two investment funds. Fund A has an average annual return of 8% with a standard deviation of 4%. Fund B has an average annual return of 15% with a standard deviation of 6%.

CV(Fund A) = (4 รท 8) ร— 100% = 50%

CV(Fund B) = (6 รท 15) ร— 100% = 40%

Even though Fund B has a higher raw standard deviation (6% vs. 4%), its coefficient of variation is lower โ€” meaning Fund B actually delivers more consistent returns relative to its own average performance than Fund A does.

Key Things to Know

  • Removes units for fair comparison: CV lets you compare the relative variability of datasets measured in completely different units or scales, which raw Standard Deviation cannot do.
  • Expressed as a percentage: because it's a ratio of standard deviation to mean, CV is dimensionless and typically reported as a percentage.
  • Breaks down near a zero mean: CV becomes unreliable or meaningless when the mean of the dataset is zero or close to zero, since it involves dividing by the mean.
  • Common in finance for risk-adjusted comparison: dividing return volatility by expected return produces a lower-is-better measure of risk per unit of reward.
  • Widely used in lab and manufacturing quality control: a low CV across repeated measurements signals high precision and process consistency.

Related Calculators

Coefficient of Variation Calculator โ†’Calculate the coefficient of variation (CV) from a mean and standard deviation instantly. Compare relative variability across datasets with different units or scales.

Related Terms

Standard DeviationStatistical Measure of Data Variability

Frequently Asked Questions

There's no universal threshold, but as a general guideline in many scientific fields a CV below 10% is considered low variability, 10-20% moderate, and above 30% high variability. The acceptable range depends heavily on context โ€” financial returns and biological measurements have very different norms for what counts as "low" variability.
Standard deviation is expressed in the same units as the original data, which makes it impossible to fairly compare variability between datasets measured in different units (like dollars vs. years) or with very different means. The coefficient of variation removes units by expressing standard deviation as a percentage of the mean, allowing direct comparison across unrelated datasets.
The coefficient of variation is typically reported as an absolute value or percentage and is only meaningful when the mean is positive and non-zero, since standard deviation itself is always non-negative. If the mean is negative or close to zero, CV becomes unstable or undefined and shouldn't be used.
In finance, CV is used to compare the risk-to-reward ratio of different investments by dividing the standard deviation of returns by the expected (mean) return โ€” a lower CV indicates a better risk-adjusted return. This lets investors compare two very different assets, such as a low-return bond and a high-return stock, on a level footing.
Manufacturing and laboratory settings use CV to assess measurement precision and process consistency โ€” a low CV across repeated measurements or production runs indicates high reliability. Many labs set acceptable CV thresholds (often under 5-15% depending on the assay) as part of quality assurance protocols.