What do I set for the standard deviation of a measurement, if the value is not normally distributed? I took multiple $B$ measurements for a constant $A$ value, which I simultaneously measured.
$A$ (in my case the resistance of a temperature sensor) was controlled by a PID controlled and slowly oscillated in the range 2596 to 2560.
It is tempting to just say that $A=2598\pm2$ but is this really correct? Because the value stayed at the turning points 2596 and 2560 the longest, not at 2598, so the "time spent" is not normally distributed over the range 2956-2600. This feels like cheating.
Or would it be best to just say $A=2560$ and don't give a statistical error at all, but only a possible systematic error due to a potential offset?
I'm really bad with these fundamental experimental questions.
 A: It doesn't have to be normally distributed. e.g. Binomial distribution also has a mean and variance (${\sigma^2}$). If you are interested in your distribution form you can plot a histogram and see it yourself. Note: not all distributions have variances (e.g. Cauchy distribution).
A: For a set of data, even if you do not know the underlying type of probability distribution, you can calculate the standard deviation of the data. This is called the standard deviation of the sample.
The standard deviation also applies for any probability distribution function, discrete or continuous: normal, binomial, exponential, beta etc. (excluding some odd ones).  This is the standard deviation of the population as opposed to the standard deviation of a sample.  The relationship for calculating the standard deviation from a sample is slightly different from the relationship for calculating the standard deviation for the population.
See any basic statistics textbook for the equation for the standard deviation for a sample that you can apply to your data (and, the equation for calculating the standard deviation for a population, and the relationships for the standard deviations for the different types of probability distributions).
