Each sample image below is a combination of 20 4-minute integrations with a StarlightXpress HX916 camera on a 6" f/5 Schmidt-Newtonian telescope with a red filter.
One single 4-minute integration (reference image):
Median combine of all 20 images
Average of all 20 images
Sum of all 20 images (note: MaximDL was used to process images -- the sum converts to floating-point values and does not exceed the 16-bit limit!):
It's obvious that the summed image has much more signal in the faint nebulosity regions of M16 than either the median-combined or averaged images do. The reason is simple: the summed image added all of the faint areas of all the images, while the faint areas just didn't have enough signal in the 4-minute integrations to rise above the background, so averaging/median combining what isn't there won't show any more! S/N levels in the average/median images are very good, but the total amount of signal doesn't compare with the summed image. The extra detail gives you much more to work with, as shown below with a little sharpening and contrast stretching:
