SD of Fitted Lognormal Distribution vs SD of Fitted Normal Distribution of Log-Transformed Data
I'd like to know why the fitted lognormal distribution for a given data set provides a different standard deviation than the fitted normal distribution of the log-transformed data set. For example, suppose I have 10 datapoints: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. When I fit the lognormal distribution, I get a standard deviation of 0.6954075. When I log transform the 10 datapoints and fit a normal distr...