A dataset has skewness = 1 with missing data. Standard deviation around median is 1.5. How much data will be unaffected?
This is not answerable in general. You don't even know the skewness or standard deviation around the median without missing data, so you can't compare those quantities. Without more information about the distribution there is no way to figure out how much data is missing, or where in the distribution the missing data is located.