3-sigma approximation I am making a system involving a sensor who has to be really precise. I found on their datasheet a diagram that shows the typical performance of the sensor. There's the mean value, the +3 sigma, respectively -3 sigma. 
I was wondering if by taking x measurements and making the average I could be sure to be close to the average?
Thanks
 A: If the lower 3-sigma limits are really computed as $\bar X \pm 3s$, where s is the sample SD, or as $\bar X \pm 3\sigma$, where $\sigma$ is some 'known' population SD, then you know $\bar X$ is the midpoint of the 3-sigma interval. If you know the sample size $n$ and it is large, then a 95% CI for the population mean is $\bar X \pm 1.96s/\sqrt{n}$. (For $s$ from a smaller sample, $n < 30$ or so, you would have
to use a number from a table of Student's t distribution insteas
of 1.96.)
If you mean by 'taking measurements and averaging' to sub-sample
from the given measurements, I see no advantage in that. The average
$\bar X$ retrieved by taking the midpoint is better than an
average you might take of a sub-sample.
All of this is, of course, subject to the assumptions of independence
and stability issues mentioned in Comments (and to my not having
totally misunderstood your question).
If you mean to take your own measurements from a population or process of your own, then I would feel
uncomfortable having you use either $\bar X$ or $s$ from a 'datasheet' obtained by a process you may not be 
replicating. In that case, use the same formula for the CI, but
totally using your own data. If the sensor is supposed to work
equally reliably for your process as for theirs, you can hope that the $s$ of your
data is consistent with the SD previously obtained. (But SD's
are hard to replicate except with huge samples, so 'consistent with'
doesn't mean 'nearly the same'. I can give you a test for that
if applicable.)
