Which is correct way to find error in degree of linear polarization?

I have a set of “degree of polarization (DOP)” values for a star.
Assume there are 10 DOP values in the set.

DOP is defined as square root of sum of squares of fractional
Stokes parameters, namely q and u, i.e.

$$DOP=P = sqrt{q^2+u^2}$$

where $q$ and $u$ are directly measured quantities; and not $P$.

I have to find error/uncertainty in this set.
I am assuming that DOP values are spread Gaussially.

My query is this:
From the following two methods, which is correct method
to find error/uncertainty in DOP?

(a) Just find RMS (standard deviation) of the 10 DOP values.
This is error in DOP set.

OR

(b) Using error-propagation technique, find individual error
in each of 10 DOP values. Then find average of these 10 individual
errors. This average is final error/uncertainty in DOP set.

Next,
Which is correct way to find average of DOP set:

(i) Just find average of 10 DOP values. 

OR

(ii) First find average of q's and average of u's and then put them in DOP definition.

In other words, does Standard Deviation/RMS has any significance when a
physical quantity is not directly measured but it is some function of another
directly measured physical quantities ?