Average Oxidation State - Utility?
It helps you when you want to balance a red-ox reaction by the mean of the oxidation number change. For example, if you want to balance the reaction of thiosulfate with iodine to tetrathionate and iodide, you realize that the average oxidation number of sulfur changed from +2 to +2.5. The oxidation half-reaction looks like this:
$$\ce{4S^{+2}-&gt; 4S^{2.5+} +2e-}$$