# Significant figures

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1. Oct 5, 2016

### emeraldskye177

1. The problem statement, all variables and given/known data

In a physics lab, Logger Pro software generated statistical estimators such as the standard deviation σ = 0.04021 of a sample of size n = 29.

Among other things, I must calculate the standard error of the mean σmean.

My question is: Must σmean have four sig figs or two (i.e., do I account for the number of sig figs in the sample size, even though n has no error associated with it)?

2. Relevant equations

σmean = σ/sqrt(n)

where σ is the standard deviation of the distribution and n is the sample size.

3. The attempt at a solution

σmean = σ/sqrt(n) = 0.04021/sqrt(29) = 0.007467 or 0.0075?

2. Oct 5, 2016

### RUber

Since your sample size is error free, you can consider that as an infinite number of sig. figs. and keep 4.

Significant figures is easiest to understand in scientific notation.
If you write it as 7.467 x 10^(-3), it is clear that this version has 4 significant figures.

3. Oct 5, 2016

### Staff: Mentor

Presumably the count is accurate and must be an exact integer. It should be treated as though it has infinite precision.

4. Oct 5, 2016

### emeraldskye177

Thanks all. In my lab report, I did it the correct way (i.e., reported the answer to 4 sig figs), but the TA docked me marks with the comment "sig figs", so I will have to take this up with the lab coordinator. Thanks again for your answers.

5. Oct 6, 2016

### Staff: Mentor

What was the number of significant digits in the data for which these σ were calculated?