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Let's say I have a set of data as follows (the mass of a sample of some chemical measured several times):

23.132 g

24.532 g

21.532 g

22.853 g

23.193 g

(I just made that data up, but imagine that a analytical scale put out those numbers, exactly as shown, on its display.)

1. When I calculate the mean, how many significant digits should the mean have?

2. When I calculate the variance, how many significant digits should the variance have?

3. When I calculate the standard deviation (by square rooting the variance), how many digits should it have?

4. When someone asks what is the mass of the sample, I know that I should tell them that the mass is: x g +/- y g. What should "x" be? Should it be the mean? If so, how many significant digits? Also, what should "y" be? I know it should be the standard deviation, but how many significant digits should it be?

5. How does the standard deviation dictate the number of significant digits of "x"?