I had to review a paper which stated:
“Antibody titers had a mean (SD) of 110 (73) ng/ml”
So a mean of 110 and a standard deviation of 73.
I immediately thought: “That’s really fishy.” The reason why I thought this is there is a very simple rule:
SD > ½ mean => data are not normal
If the standard deviation is larger than half of the mean you can conclude that the data are not normally distributed. This simple rule only applies when negative values are not allowed.
So I knew immediately that the data in the paper were not normally distributed and as a result median and IQR were more appropriate to describe the data than mean and SD.