Coefficient of Variation Calculation Formula

Coefficient of Variation Formula:

\[ CV = \frac{\sigma}{\mu} \times 100 \]

Coefficient of Variation (CV):

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1. What is the Coefficient of Variation?

The Coefficient of Variation (CV) is a standardized measure of dispersion of a probability distribution or frequency distribution. It shows the extent of variability in relation to the mean of the population.

2. How Does the Calculator Work?

The calculator uses the CV formula:

\[ CV = \frac{\sigma}{\mu} \times 100 \]

Where:

\( \sigma \) — Standard deviation of the dataset
\( \mu \) — Arithmetic mean of the dataset

Explanation: The CV expresses the standard deviation as a percentage of the mean, allowing comparison between datasets with different units or widely different means.

3. Importance of CV Calculation

Details: CV is particularly useful when comparing the degree of variation from one data series to another, even if the means are drastically different from one another.

4. Using the Calculator

Tips: Enter standard deviation and arithmetic mean in the same units. The mean must be greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a good CV value?
A: Generally, a CV < 15% is considered low variability, 15-30% moderate, and >30% high variability, but this depends on the field of study.

Q2: Why use CV instead of standard deviation?
A: CV is unitless and allows comparison between datasets with different units or scales.

Q3: When shouldn't I use CV?
A: When the mean is close to zero (can produce misleading high CV) or when working with interval scales that have a true zero.

Q4: How does CV relate to precision?
A: In analytical chemistry, CV is often used as a measure of precision (repeatability) of an assay.

Q5: Can CV be greater than 100%?
A: Yes, when the standard deviation is larger than the mean, the CV will exceed 100%.