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Sample Variance (s²)
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Mean (x̄)
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Std. Deviation
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Count (n)
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Sum (Σx)
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Minimum
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Maximum
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Range
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Sum of Squares
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Coeff. of Variation
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What Is a Coefficient of Variation Tool?
A coefficient of variation (CV) calculator measures the relative variability of a data set by expressing the standard deviation as a percentage of the mean. Unlike standard deviation alone, CV is dimensionless — it does not depend on the unit of measurement — which makes it ideal for comparing the spread of data sets with different scales or units. For example, you can meaningfully compare the consistency of height data measured in centimetres with weight data measured in kilograms. A lower CV signals tighter clustering around the average, while a higher CV indicates greater relative dispersion.
Formula
The coefficient of variation normalises spread relative to the central tendency.
Coefficient of Variation
CV = (σ / μ) × 100%
CVCoefficient of variation (expressed as a percentage)
σStandard deviation (population or sample)
μMean (use |μ| if the mean can be negative)
How to Calculate the Coefficient of Variation Step by Step
Compute the mean.Sum all values and divide by the count: μ = Σxᵢ / N.
Compute the standard deviation.Find σ (population) or s (sample) using the standard formula.
Divide SD by the mean.Calculate the ratio: σ / μ.
Multiply by 100.Convert the decimal to a percentage: CV = (σ / μ) × 100%.
Solution:Instrument A — Mean = 5.016, SD ≈ 0.011, CV ≈ 0.22%. Instrument B — Mean = 5.00, SD ≈ 0.158, CV ≈ 3.16%.
Answer:Instrument A (CV ≈ 0.22%) is far more precise than Instrument B (CV ≈ 3.16%)
3Annual Rainfall in Two Cities
Data:City X (mm): 800, 850, 780, 820, 810 | City Y (mm): 200, 350, 150, 280, 220
Solution:City X — Mean = 812, SD ≈ 24.9, CV ≈ 3.07%. City Y — Mean = 240, SD ≈ 72.1, CV ≈ 30.03%.
Answer:City Y has much higher relative rainfall variability (CV ≈ 30%) than City X (CV ≈ 3%)
How to Use This Coefficient of Variation Calculator
Follow these simple steps to get your CV percentage:
Enter your data values separated by commas, spaces, or line breaks.
The calculator computes the mean, standard deviation, and CV percentage automatically.
Compare CV values across different data sets to determine which is relatively more variable.
Use the step-by-step breakdown to verify intermediate calculations.
Benefits of Using a CV Calculator
Enables apples-to-apples comparison of variability across data sets with different units.
Quickly identifies which data set or process is most inconsistent.
Essential for quality control where tolerance specifications use relative measures.
Removes the need for manual intermediate calculations (mean → SD → ratio).
Helps researchers determine measurement reliability in experimental studies.
Where the Coefficient of Variation Is Commonly Used
Laboratory Science
Assessing assay precision — CV < 5% is often the benchmark for acceptable reproducibility.
Finance
Comparing risk-adjusted returns of different portfolios or asset classes.
Manufacturing
Evaluating production consistency across machines or shifts.
Agriculture
Measuring crop yield variability across fields or seasons.
Ecology
Comparing population size variability among species with vastly different abundances.
Clinical Trials
Determining inter-patient variability in drug response or biomarker levels.
Interpreting CV Across Different Fields
A "good" CV is not a fixed number — it depends entirely on your discipline and application. Here is a field-by-field guide:
Analytical Chemistry (CV < 5%)
Regulatory bodies like the FDA expect CVs below 5% for validated bioanalytical methods. A CV above 15% usually means the method needs re-validation.
Manufacturing (CV < 10%)
Process capability indices (Cp, Cpk) are closely related to CV. A CV under 10% generally indicates a capable process for most industries.
Finance (CV context-dependent)
A stock with a CV of 30% may be considered moderate risk. In fixed-income portfolios, the same CV would signal extreme volatility.
Ecology & Biology (CV 15–50% common)
Natural variability is inherently higher in biological systems. CVs of 30% or more are normal for wildlife population counts.
Survey Research (CV < 20%)
For survey-based metrics, CVs above 20% suggest the questionnaire item may not be reliably measuring what it intends to.
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Frequently Asked Questions — Coefficient of Variation Calculator
Everything you need to know about variance.
What is the coefficient of variation (CV)?
The coefficient of variation (CV) equals (standard deviation / mean) × 100%. It measures relative variability — how large the spread is relative to the average. A CV of 10% means the standard deviation is 10% of the mean. CV is useful for comparing variability between datasets measured in different units or scales.
How do you calculate the coefficient of variation?
To calculate CV: 1. Calculate the mean (x̄). 2. Calculate the standard deviation (s or σ). 3. Divide: CV = (standard deviation / mean) × 100%. For example, if mean = 50 and SD = 5, then CV = (5/50) × 100% = 10%. Use the absolute value of the mean if it could be negative.
What is a good coefficient of variation?
Generally: CV < 15% indicates low variability (good consistency). CV 15–30% indicates moderate variability. CV > 30% indicates high variability. However, what's "good" depends on the field. In laboratory testing, CV < 5% is expected. In ecological studies, CV > 30% may be normal. In manufacturing, lower CV means more consistent output.
When should you use CV instead of standard deviation?
Use the coefficient of variation when: 1. Comparing variability between datasets with different units (e.g., height in cm vs weight in kg). 2. Comparing datasets with very different means. 3. Assessing measurement precision across different scales. Standard deviation alone can be misleading when means differ significantly — CV normalizes the spread relative to the mean.
Can the coefficient of variation be greater than 100%?
Yes. A CV > 100% means the standard deviation exceeds the mean, indicating very high relative variability. This can happen with highly skewed data, data with values near zero, or data sets with extreme outliers. For example, income distributions in some populations can have CV > 100%.
What is the difference between coefficient of variation and variance?
Variance measures absolute spread in squared units. Coefficient of variation measures relative spread as a percentage of the mean. Variance depends on the scale of your data — doubling all values quadruples the variance. CV is scale-independent — doubling all values leaves CV unchanged. This makes CV ideal for cross-dataset comparisons.