When two balanced dice are rolled, the sum of the dice can be 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12, giving 11 possibilities. therefore the probability is 1/11 that the sum is 12?

False.

There are 36 possible outcomes, corresponding to numbers 1-6 independently appearing on each of the dice. Only one of those outcomes is double-sixes, resulting in a sum of 12. The probability that the sum is 12 is 1/36.

In short, the 11 outcomes listed in your problem statement are not equally-likely.

Measure of mean. When there are no outliers and the data seems symmetric then the mean and the standard deviation are used to measure the center and the spread. 

The only reason I believe it's be measure of mean is because even with the exact data, the only gap between the numbers would be a maximum of 10 and that still wouldn't be an outlier. Because of this, the mean would be the best measure of center since the data won't be skewed, only symmetric.