In a perturbed system, writing the equations of motion in a form where the contribution of fast variables is replaced by their average on the corresponding invariant torus.
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Generally, yes, because the averaging removes the effects of random errors in the measurements. However if your measurement technique has biases, these will not be removed through averaging and the averaged result will be biased.
Yes, if you are averaging numbers that include negative numbers.
You add them and divide by two. (Also known as averaging them)
Counting Principle is one of them