Can measurements be made more precise then the measuring device?

[mrspeedybob]

Suppose there is a quantity X to be measured. To do this you have a measuring device with a resolution of 1 and an accuracy of +/-1. It is imediately obvious that repeated measurements can yield an accuracy of +/- 0.5 but can any greater certainty be achieved?

If 2 measurements are made and they are, for example 6 and 7, then it can be stated that 5<=X<=7 for the first measurement and 6<=X<=8 for the second so 6<=X<=7 so X=6.5 +/- 0.5. What if 10 measurements were made and 9 came up 6 but only 1 came up 7. Can it be stated with any degree of certainty that X is closer to 6 then to 7?

 

[Bill Simpson]

"An Introduction to Error Analysis" by John Taylor is a good book.

If you can characterize the error of the instrument, perhaps something more specific than it has an accuracy of +/-1, then averaging the measurements can give you significantly more accuracy. The book describes it all. If you are interested in this subject it should be a fascinating read.