Question

If we take the average of our readings how does error get reduced ?

Answer 1

Averaging actually doesnt reduce the error in the readings.What actually we do in an experiment is that we take a number of readings to account for the error that might occur in readings.This will help you to get a wide range of results.And when we take the average of that, there is more chance that the actual value lies near to the average value. A mean/average is likely to be more accurate than half of your measurements (pretty much by definition, but of course the problem is that you won't know WHICH ones are off). You could be way off in all cases and just have a mean that is better than half the measurements. So increasing the number of readings will simply make the standard deviation small and thereby make the result more accurate(by reducing the error)