I have seen in papers that for the data of a skewed distribution, it was interpreted as median ± SD. Here, does this SD represents SD of mean? Why don't using median (P25,P75) for data of skewed distribution?
If you are arguing that it only makes sense to report an SD with a mean rather than a median, then I agree with you.
The quartiles are similar to the median in the sense of reporting measurements taken at observed frequency. In the median we consider halves and in the quartiles, four parts.
I think the option you suggest is interesting, since the quartiles Q1, Q2, Q3 are an "extension", so to speak, of the median, where P25: first quartile, P50: median, P75: third quartile.
Regarding your question: Here, does this SD represent SD of mean?
As I understand it, SD refers to median, not media and in the case of a skewed distribution: if mean > median, the distribution is skewed to the right and if mean < median, the distribution is left skewed.
I think perhaps the reason for choosing the median is to be somewhat insensitive to atypical data.
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