In statistic, the Coefficient of variation formula or known as CV, also known as relative standard deviation (RSD) is a standardized measure of dispersion of a probability distribution or frequency distribution. When the value of coefficient of variation is lower, it means the data has less variability and high stability.
The formula for coefficient of variation is given below:
\[\LARGE Coefficient\;of\;Variation\;Formula = \frac{Standard\;Deviation}{Mean}\]
As per sample and population data type, the formula for standard deviation may vary –
\[\large Sample\;Standard\;Deviation=\frac{\sqrt{\sum_{i=1}^{n}(X_{i}-\overline{X})^{2}}}{n-1}\]
\[\large Population\;Standard\;Deviation=\frac{\sqrt{\sum_{i=1}^{n}(X_{i}-\overline{X})^{2}}}{n}\]
x_{i} = Terms given in the data
$\overline{x}$ = Mean
n = Total number of terms.
Regular Test Â Â Â Â Â Â Â Â | Randomized Answer | |
Mean | 59.9 | 44.8 |
SD | 10.2 | 12.7 |
Trying to compare the two test results is challenging. Comparing standard deviations doesnâ€™t really work, because the means are also different. Calculation using the formula CV=(SD/Mean)*100 helps to make sense of the data:
Regular Test Â Â Â Â Â Â Â Â | Randomized Answer | |
Mean | 59.9 | 44.8 |
SD | 10.2 | 12.7 |
CV | 17.03 | 28.35 |
Looking at the standard deviations of 10.2 and 12.7, you might think that the tests have similar results. However, when you adjust for the difference in the means, the results have more significance:
Regular test: CV = 17.03
Randomized answers: CV = 28.35