To find the standard deviation of a group of numbers, we not only need to know the average of the set, but also the distance of each term from the average.

Statement (1) is insufficient. We know that every term is either 2 or 3, but without knowing how many there are of each, we can't find the average or the distance of each term from that average.

Statement (2) is also insufficient. 8 of the terms are equal, but we don't know how the other four terms relate to those eight equal terms. A set with 8 2's and {10, 11, 12, 13} has a very different standard deviation from one with 8 2's and {3, 3, 3, 3}.

Taken together, the statements are sufficient. If all of the terms are either 2 or 3 and 8 of the terms are the same, the set includes either 8 2's and 4 3's or 8 3's and 4 2's. In the first case, the average is 2 1/3; in the second, the average is 2 2/3. It may seem like that is insufficient, but remember we're looking for the standard deviation, not the average.

If there are 8 2's and 4 3's, the average is 2 1/3. 8 of the terms are 1/3 away from the mean and the other 4 are 2/3 away from the mean. If there are 8 3's and 4 2's, the average is 2 2/3. Again, 8 of the terms are 1/3 away from the mean and 4 are 2/3 away from the mean. The terms used in calculating standard deviation are those "distances from the mean." In both cases, those distances are the same, so the standard deviation is the same in either case. Choice (C) is correct.