When you have two pieces of the same data, and you average it, what happens to the uncertainty. (details pls)?

The uncertainty goes down. There are mathematical definitions (standard deviation is the most useful here), but with two measures, it seems just common sense is most appropriate. There is variation in everything (scientists speak a lot about bell-shaped curves, with lots of individuals (or pendulum swings) near the average, and fewer at the extremes). If you select one entry, you get one value from that curve. You can't say if you selected one from near the average, or one from the extreme types. If you select two entries, the odds of selecting two extreme cases goes way down. The most individuals are at the peak of this bell shaped curve, which is the average of the population, if such a curve represents the population well. The more samples you have, the closer your average will be to the real value.