I work with cost data and I have been made to believe that Median is better as it is the central to the distribution. However, what about of the weight of distribution.
What I think is that taking Mean(SD) will be better. The mean will determine the central value and the SD will take care of the values spread across that mean. So, it is a better representation of your data. Also, you can take the standard error for more accuracy.
The Median (IQR) will give you a range but that may not represent the true fact about the data. Some of the important values might get missed. And bias ness will automatically be incorporated.
You need both the mean and median.
Use only the median if the data is highly skewed and if there are very large and low values in the data. Use the mean if the data has low skewness and if there are no distortionary outliers (i.e. extremely large and small values)
Both can be used and depend on the author's opinion to study the study population, but the use of the mean is more common.
Am more comfortable with the mean when the data has a low skewness. However median can be good for data with large extremes
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