Here's an idea of what you should do:
width = XX
height = YY
#crops to (x1,y1) to (x2,y2) when x2>x1 and y2>y1
frame = img[width/4:(width/4+width/2), height/4:(height/4+height/2)]
And then,
r = np.array(frame[:,:,0])
avg_r = np.average(r)
Repeat for G and B.