The median is obtained by applying the inverse transformation to the estimated mean of the transformed data.
Example:
If the natural logarithm of the measured pollution level is normally distributed with mean µ and variance σ2, the mean of the original variable is exp{µ + ½ σ2} whereas its median is exp{? }. For µ = 3 and σ2 = 1, the mean is exp{3.5} = 33.1 and the median is exp(3.0) = 20.1.
An exact algorithm for confidence interval estimation of the lognormal mean and, more generally, for linear functions of the normal mean and variance, has been known for some time but its application has involved some rather tedious calculations based on tabulated data.
The computer algorithm developed by Brad Lyon of Oak Ridge National Laboratory and Charles Land of the Radiation Epidemiology Branch, NCI, is very fast and has been extensively tested for accuracy.