I'm calculating a value based on experimental data. The calculation is
$$ k = \frac{a - b}{c} \cdot \frac{1}{T}, $$
and $a$, $b$ and $c$ are all measured experimentally, multiple times, with some variation between samples, and $T$ is a constant. They are also measured independently, so even if I happen to have $N$ values each of $a$, $b$, and $c$, I cannot say that they "belong" to each other in triples, or anything like that.
What is the correct way of calculating the standard deviation in the result $k$? I believe I can not-totally-unreasonably assume that $a$, $b$, and $c$ are normally distributed, although strictly speaking the numbers are all constrained (both in reality and in the measurements) to be positive, so they are not truly normal.
(I tried calculating $k$ from all permutations of my different values of $a$, $b$, and $c$. Say $N = 4$, then I have $4 \times 4 \times 4 = 64$ different combinations I can use to calculate $k$, and then I can take the standard deviation of that. It feels a bit like a hack, though, so some theoretical insight would be nice.)
Just to provide a more concrete example, here are some numbers (in the form of python code, for convenience). These are obtained from measurements, where the values of $a$ measured from four different samples, $b$ from four other samples, and $c$ from yet another four samples.
a = np.array([286641, 266093, 227900, 165559])
b = np.array([136748, 159846, 108337, 164340])
c = np.array([303791, 327579, 410016, 340820])
T = 5
So the question then becomes: Give these data, and given that $k$ is calculated from the equation above, what, if anything, can I say about the standard deviation (or other ways of communicating uncertainty) in my calculated values of $k$.
