1. Meaning of Coefficient of Variation
The coefficient of variation (C.V.) measures how large the standard deviation is compared to the mean. It is a relative measure of dispersion, which means it helps compare the variability of two or more data sets even if their means are different.
A smaller C.V. means the data is more consistent. A larger C.V. means the data is more scattered.
2. Formula for Coefficient of Variation
The formula for C.V. is:
\( C.V. = \left( \dfrac{\sigma}{\bar{x}} \right) \times 100 \)
Here:
- \( \sigma \) = standard deviation
- \( \bar{x} \) = mean
- C.V. is expressed as a percentage
3. Purpose of C.V.
C.V. helps compare the variability of two sets of data that may have different units or different means. It shows the scatter in proportion to the average.
It is commonly used when comparing performance, consistency, stability, or risk.
4. Example
Consider two runners whose lap times (in seconds) have the following statistics:
- Runner A: Mean = 60, Standard deviation = 6
- Runner B: Mean = 50, Standard deviation = 8
Compute their C.V. values:
\( C.V._A = \dfrac{6}{60} \times 100 = 10\% \)
\( C.V._B = \dfrac{8}{50} \times 100 = 16\% \)
Although Runner B has a faster average time, Runner A is more consistent because his C.V. is smaller.