As a verb, to mean is to intend or to signify something. As an adjective, mean can describe someone who is unkind or something that is small or poor in quality. As a noun in math, the mean is the average value of a set of numbers.
The 'intend/signify' verb comes from Old English “mǣnan” meaning 'to intend, to signify'. The 'unkind' adjective comes from a different Old English root meaning 'inferior or common', which later shifted to moral judgment. The mathematical 'mean' comes from Latin “medianus” and Old French “meien” meaning 'middle'.
English crammed at least three different histories into 'mean': intention, meanness, and mathematical middle all come from separate roots. That’s why context matters so much—'I mean it', 'she’s mean', and 'the mean is 10' are strangers wearing the same spelling.
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