I have a dataset, always considered log-normally distributed, from which I calculate a median value (0.735). In a book, I have seen someone using similar data but calculating related median value by taking the antilog of the mean of log10 of these data. I get 0.69 instead with this method.
What is the point of using this type of antilog method in general?
At the end, I would like to create a cumulative distribution curve based on the median value to calculated the chances (P25, P50 and P75) of having certain values of my dataset.