# Question on significant digits

Hi all.

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"?

## Answers and Replies

The mean has 3 significant digits. The error in Mean^2 is 2* mean * the error in the mean. The variance has the same no. of significant digits as Mean^2.
Perhaps you'd like to look up Error Analysis.