What are some uses of the overall colour average of an image?
Well, I can't honestly say that I ever used it, there was a moment when I was considering doing something similar for some quick-and-dirty "shadow" correction.

My friends showed me a flight video, where in the middle of the video there was some dark patches in every frame due to their propeller. To me it looked like a patch in very dark shadow (I never actually got to play with the video so I can't be certain - if the patches actually were the way I suppose or if this would work).

If I didn't want to do any serious correction technique but just spend a bit of time on it for myself, here's what I would do:


calculate the color average of the image $avg_{img}$
find the darker connected areas (the "shadowed" part in each frame) and calculate their average $avg_{dark}$
for all the pixels in the darker area, take their difference from $avg_{dark}$  and add it to $avg_{img}$ and replace their value with this new one
hopefully, result would be a video that's still flawed but somewhat easier to watch than the one with dark propeller-patches flying around in the middle