Explanation

In this question, and anywhere we are dealing with standard deviation, the key is "dispersion." In mathematical terms, the quantity called dispersion is the square of the standard deviation, but more to the point, the standard deviation is a measure of dispersion of points. For that reason, we generally have to know all the values in a set to calculate the set's standard deviation, but we can also check more conceptually whether we are getting the full measure of the dispersion. Finally, we can attempt to apply the precise formula for standard deviation if that is required. Okay, on to the data statements, separately first.

Statement (1) tells us what the points are dispersed around, but not how dispersed they are. Everyone's value could be 6 and there would be no deviation at all, or the points could vary widely. Both cases are permitted by Statement (1) and yield different standard deviations, so Statement (1) is insufficient.

Statement (2) gives us dispersion information--it says that there is no dispersion! We don't know around what point the dispersion (non-dispersion, in this case) is centered, but standard deviation doesn't measure that. So, in fact, the standard deviation must be zero. Statement (2) is sufficient. When we first glanced at the answer choice, we would have been tempted by a "together" answer, but fortunately we were careful to evaluate the choices separately first.

The correct answer is (B).