I'm having trouble imagining what variance and deviation mean with a series of die rolls. That is, a fair die will fall with a flat distribution on all its values 1-6. Does the concept of variance really make sense on a uniform distribution? [Edit: Is it like asking "What is the variance of white noise?"]
The mean will be 3.5, but what is the variance and deviation values? Is this question even valid in an ideal setting? It seems the variance and standard deviation tacitly ASSUME an a priori normal distribution around an unspecified or unknown order -- but a perfectly flat distribution (as n-> infinity) with no other hidden variables has no variance (or shouldn't have any).
[Edit: The question is confusing because it changes the standard orientation of the dependent vs. independent axiis. Knowing the "mean" here misinforms the intuition. What you need to understand the question is the idea of 6 different "bins", each with a count of how many times the die has landed there. The face values aren't the independent axis, even though they don't change. The number of rolls is the independent axis. See my answer below.]