I understand that with log-transformed data, the coefficient of variation (CV) on the original scale is equal to
sqrt(exp(sigma^2)-1), where sigma is the standard deviation of log-transformed data.
But is there anything inherently wrong with simply calculating CV on log scale as
xbar is the mean of the log-transformed data?
For instance, would this calculation of CV on log-scale not really represent what is thought of as a coefficient of variation?
EDIT to explain my intended use of CV
My intended use is to report descriptive statistics for two sets of data:
- price data for homes in different cities in Europe and;
- price level indexes of homes for different cities in Europe using London as
a 'base', i.e.
(price home in city x/price home in London) x 100.
Because city prices and indexes generally, but not always, follow a log-normal distribution I decided to perform a log transformation to better visualize the distance of each city price or each city price level index from the center of each respective distribution.