Uncertainty in Average Intensity Calculation

[maves]

Homework Statement

I am analysing intensities of some pictures. There are specific regions of higher intensities and so far i have managed to locate those regions automatically in Mathematica and the program returns the average intensity and standard deviation on this regions ("circles"), so I can also determine the number of circles.

Homework Equations

I would like to calculate the average intensity of the whole picture and its uncertainty. How can I make this, using mean values of intensity and their deviations (uncertainties)?

The Attempt at a Solution

To get the average value of the whole picture, I of course use the formula for average on my measured mean intensities:
$$x_{avg}=\frac{1}{N}\sum_i x_i\,.$$
But what about the error? One way would be to calculate standard deviations of these mean intensities regarding the calculated "mean of the mean", using a standard formula for std.dev.:
$$\sigma=\sqrt{\frac{1}{N}\sum_i(x_i-x_{avg })^2}$$
If this is correct, should it be N-1 in the denominator? And for error i use $$\Delta x=\sigma/\sqrt{N}$$?
But that does not anyhow include the uncertainties of my measurements that I already have (and I also don't think it's ok as my circles are not of equal size). I believe that the uncertainties should be used somehow-? But the "average" of those uncertainties doesn't seem to be the right way.

Please help.

 

[Greg Bernhardt]

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?