The modern senses have arrived since the 18th century. Shakespeare uses earlier senses expressing nuances of inferiority. When Lady Grey says to Edward "I am too mean to be your queen" (Henry VI Part 3, III.ii.97), she means "of low rank", and when we read the stage direction telling Lucentio to enter "in the habit of a mean man" (The Taming of the Shrew, II.i.39), it means "lowly, humble". We have to be careful not to let the modern senses interfere, especially in such phrases as "mean woman". A further negative meaning is "unworthy", as when Helena refers to herself as someone "too meanTo have her name repeated" (All's Well that Ends Well, III.v.59).
And Americans especially have to beware not to read in their modern positive sense, as when Katherina talks about "a very mean meaning" (The Taming of the Shrew, V.ii.31).
David Crystal is author, with Ben Crystal, of Shakespeare's Words, published by Penguin