Significant figures

Homework Statement

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)?

Homework Equations

σmean = σ/sqrt(n)

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

The Attempt at a Solution

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

RUber
Homework Helper
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.

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

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.

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