Coefficient of Variation Calculator

Coefficient of Variation Formula:

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

Coefficient of Variation (CV):

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1. What is Coefficient of Variation?

The coefficient of variation (CV) is a standardized measure of dispersion of a probability distribution. It shows the extent of variability in relation to the mean of the population. It's often expressed as a percentage.

2. How Does the Calculator Work?

The calculator uses the CV formula:

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

Where:

\( \sigma \) — Standard deviation
\( \mu \) — Mean

Explanation: The CV is calculated by dividing the standard deviation by the mean and multiplying by 100 to express it as a percentage.

3. Importance of CV Calculation

Details: CV is particularly useful when comparing the degree of variation between data sets with different units or widely different means. It's commonly used in quality control, finance, and laboratory measurements.

4. Using the Calculator

Tips: Enter the standard deviation and mean values. Both must be positive numbers (mean cannot be zero). The result will be displayed as a percentage.

5. Frequently Asked Questions (FAQ)

Q1: What does a high CV indicate?
A: A high CV indicates greater variability relative to the mean. The acceptable range depends on the application.

Q2: When should I use CV instead of standard deviation?
A: Use CV when you want to compare variability between data sets with different units or significantly different means.

Q3: What is a good CV value?
A: In laboratory settings, CV < 10% is generally acceptable, but this varies by field. Some applications may require CV < 5%.

Q4: Can CV be negative?
A: No, since standard deviation and mean are always non-negative (with mean > 0), CV is always non-negative.

Q5: What are limitations of CV?
A: CV shouldn't be used when the mean is close to zero, as it can become very large and misleading. It's also not meaningful for interval scales that don't have a true zero.