What is the meaning of the word "mean"?

Definitions:

A condition, quality, or course of action equally removed from two opposite extremes. NOUN
- The mean between two extremes.
Be of some specific importance to someone, especially as a source of benefit or object of affection. VERB
- Animals have always meant more to him than people.
Design or destine for a particular purpose. VERB
- The jacket was meant for a much larger person.
Equally far from two extremes. ADJECTIVE
- Hope is the mean virtue between despair and presumption.
Genuinely intend to convey or express something. VERB
- When she said that before, she meant it.
Intend something to occur or be the case. VERB
- They mean no harm.
Intend to convey, indicate or refer to a particular thing or notion; signify. VERB
- I don't know what you mean.
Of a word, have something as its signification in the same language or its equivalent in another language. VERB
- Its name means "painted rock" in Cherokee.
Poor in quality and appearance; shabby. ADJECTIVE
- Her home was mean and small.
The value obtained by dividing the sum of several quantities by their number; an average. NOUN
- Acid output was calculated by taking the mean of all three samples.
Unkind, spiteful, or unfair. ADJECTIVE
- The teacher was mean to the students who struggled with the material.