smc

The average of a list is the sum of all numbers divided by the size of the list. The sum of the list can be found by adding the numbers in pairs: $(1+-2)+(3+-4)+...+(199+-200)$ The sum of each pair is $-1$, and there are $100$ pairs, so the total sum is $-100$. There are $200$ numbers on the list, so the average is $\frac{-100}{200}=-0.5$, and the answer is $\boxed{-0.5}$