Question

a population has a mean of 100 and a standard deviation of 20. If you select a single score from this population, on average, how close would it be to the population?

Answer 1

On average it would be 0 from the mean, as this is the meaning of the mean.

If the question is the mean absolute difference mean|x- 100|,
then the problem is harder.

The mean of the squared differences (x - 100)^2
is the definition of the variance, the square of the standard deviation.