Coefficient of Variation The coefficient of variation (CV) is a measure of how much the value of a variable varies relative to its mean. It is calculated by...
Coefficient of Variation
The coefficient of variation (CV) is a measure of how much the value of a variable varies relative to its mean. It is calculated by dividing the standard deviation by the mean.
Formula:
CV = Standard deviation / Mean
Interpretation:
A high CV indicates that the value of a variable is highly variable relative to its mean.
A low CV indicates that the value of a variable is relatively consistent relative to its mean.
Examples:
If the mean of a variable is 100 and the standard deviation is 10, then the CV would be 10/100 = 0.1. This means that the value of the variable can vary by up to 10 units around the mean.
If the mean of a variable is 100 and the standard deviation is 5, then the CV would be 5/100 = 0.05. This means that the value of the variable can vary by up to 5 units around the mean.
Applications:
The coefficient of variation can be used to compare the dispersion of different variables.
It can also be used to assess the impact of changes in the mean on the variability of a variable.
Additional Notes:
The coefficient of variation is a dimensionless quantity, meaning that it does not have units.
It is often expressed as a percentage.
A CV of 0 means that the variable is perfectly constant, while a CV of 1 indicates that the variable is completely uncorrelated with the mean