What is the standard deviation of a set of numbers whose mean is 20?

I think Statement 1 means to say that each element in the set is the same distance from the average (Statement 1 doesn't make sense as written -- for one thing, if it means to say several numbers are equal to each other, the verb needs to be plural).

Even using both Statements, we don't have nearly enough information to compute the standard deviation. If every value in a list is the same distance from the mean, then that distance is the standard deviation. So, for example, in this list:

14, 14, 14, 26, 26, 26

where each value is 6 from the mean, the standard deviation is 6. So Statement 1 tells us something potentially useful, but Statement 2 is not nearly enough help. Here, the standard deviation can really be anything greater than zero; the inequality in Statement 2 can't possibly let us compute an exact value of it.