I have a series of repeated measurements of light intensity at different points on a grid. I have made a histogram for each point showing the relative difference between modelling and measurement. My histograms are fairly close to normal with a mean of zero. I am using the standard deviation of this distribution to quantify the width of this distribution for each point on the grid. Ideally I would now like to combine all of these standard deviations into one figure to describe the entire grid.
Is there a better way of doing this than simply finding the mean of all standard deviations? I don't want to assume that each point is ultimately a sample of the same population distribution (although in practice if there are significant advantages to doing so then pragmatically its probbaly not far from true). There is an equation at the bottom of the wiki page on standard deviations but I have never seen it before and no references are given.
My question may be a repeat of Determining true mean from noisy observations, but I wasn't sure if that was assuming that each point was a sample from the same population.