Non-random observations (regarding physical quantity)? Are there completely deterministic observations? More detailed: Talking about an observations process for which of the following sentences would you vote:
Version 1 (always random): "These observations are the outcome of a stochastic process."
Version 2 (sometimes deterministic): "In many cases, these observations are the outcome of a stochastic (or sufficiently chaotic) process."
My teacher prefers version 1, but he could not convincingly prove that all observations are the outcome of a stochastic process. On the other hand I could not provide a non-random counterexample neither.
I hope the question is understandable somehow, since I am not a physicist...
Edit: After reading the question this morning, I have decided to specify the context a little further: I am writing a brief explanation about "measuring principles" and the sentence before the two versions above is "Methods to estimate physical quantities always rely on observations." So I am talking about any observations one could interpret as observation in order to measure anything...
 A: Ok, let me state, that both are correct.
And i explain why:
Determinism is either total or there is no determinism. Determinism means that one can determine everything that one wishes with any accuracy desired. This is a by definition a total statement.
As such determinism is total. Partial determinism is just another name for in-determinism. Exactly because determinism is a total statement.
So in this sense Version 1 is correct.
But so is version 2. because partial determinism is effectively in-determinism. Plus in-determinims does not mean that nothing can be calculated or estimated (to some accuracy).
If this was the case science (and causality) would have no application (and implication)
So in this sense Version 2 is also correct.
These things that function as conditions on a physical process (related to causality for example), i would refer to them as compatibility conditions for a process, in some cases these are refered as conservation laws. In some cases, one can see these conditions, as manifestation of causality in indeterminism.
This view above is not standard (or endorsed) as far as i know. So read it as such.
A: The "authority" that decides the answer to your question is the WAVE-FUNCTION.
So, it can create different situations:
1) If the wave-function is a given eigenfunction of the observable that you measure, the answer is deterministic and equal to the eigenvalue corresponding to that eigenfunction.
2) If the wave-function is not as in the case 1, then the answer is stochastic, with the distribution of probabilities of the different answers as predicted by the absolute square of the wave-function.
3) But there exists a 3rd, tricky case - entanglements. Did you learn of them?
Let's take for instance, taking the spin singlet, which is an entanglement of two fermions, each one of spin 1/2 . Assume that each fermion is observed by a different observer, let's name them observer Alice and observer Bob. Each observer picks some direction in the space and measures the spin projection of his fermion along that direction. The result can be either -1/2, or +1/2 .
Now, consider the particular case that Alice and Bob pick the same direction in space. 
If they don't communicate with one another, each one gets random results.
But if, say, Alice communicates to Bob what she got, Bob knows now with precision what will be his result: opposite to that of Alice.
Good luck,
Sofia 
