Suppose you are given a data set which has missing values spread along 1 standard deviation from the median. What percentage of data would remain unaffected and Why?

Since the data is spread across the median, let’s assume it’s a normal distribution.
As you know, in a normal distribution, ~68% of the data lies in 1 standard deviation from mean (or mode, median), which leaves ~32% of the data unaffected. Therefore, ~32% of the data would remain unaffected by missing values.