- #1
sloane729
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Homework Statement
This has been bothering me for quite a while. I'm trying to work out how many measurements I will need to make to get my uncertainty under a predetermined value. If say I want the a fractional uncertainty [tex]\frac{\delta T}{T}[/tex] to be equal to or under some value for some timed event, how would I calculate the number of trials I will need to make to get that uncertainty.
Homework Equations
the standard deviation of some quantity to be measured T is
[tex] s = \left( \frac{1}{N-1}\sum_i (T_i - \overbar{T})^2 \right)^{1/2} [/tex]
then
[tex] \delta T = u = \frac{s}{\sqrt{N}}[/tex]
The Attempt at a Solution
Since to calculate the uncertainty [tex]\delta T[/tex] I would need first find the average of all values of [tex]T_i[/tex] then find the standard deviation divided by the square root of the number of trials which is equal to[tex]\delta T[/tex]. But the number of trials is what I need to find but I can't know it without first finding the average value which is not possible because I need the number of trials etc. It seems like a round about problem if I'm not mistaken