Question on significant digits

  • Thread starter solarwind
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  • #1
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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

  • #2
336
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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.
 

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