When we suggest that something is 'mean', we tend to disassociate the meaning 'to be average' with nastiness, lack of generosity or cruelty.
But if we think about it - these terms are linked. When we lack generosity we might only be giving the average and not over stretching ourselves. When we are being nasty, we are detracting from an abundance of possibilities and belittle that person. When we are cruel, the cruelty lies in hindering the other person, stopping them from fulfilling their nature or full potential.
To be mean is about control. By controlling something, we limit and inhibit. That 'the mean' is one form of average used in math, indicates something about the nature of mathematics and the naming of entities.
Think of the following statement: "On average, a UK citizen will cheat on their spouse twice in their lifetime."
This tells us nothing of the many instances of 'cheating', nor about the various reasons why people might actually cheat. The statement lacks imagination. Nor does it question what is meant by cheating or why couples choose to make a commitment to each other. This statement really is mean.