Three jobs, three ancestries
English speakers use mean for intending, for unkindness, and for a midpoint. Those jobs share a sound and a spelling. They do not share a history. Tracing the origin of the word mean is a matter of keeping three files apart: a native verb of intending, a native adjective that once meant shared, and a French loan for what sits in the middle.
Having it in mind
The verb is the oldest of the three in English. Old English already had mǣnan, used both for planning to do something and for the sense a word or speaker conveyed. Middle English kept the verb as menen. The modern past meant still shows the old weak-verb pattern rather than a later analogical meaned.
West Germanic relatives stay close in form and sense: Dutch menen, German meinen, Old Saxon menian, Old Frisian mena. Behind those sits a reconstructed Proto-Germanic mainijaną, from an earlier meino- that named opinion or intent. Some accounts tie that noun to the Indo-European root for thinking that also yields English mind. Others, including the American Heritage treatment, stop at mei-no- and do not force the link. The point of agreement is narrower and safer: this verb is inherited Germanic, not a later borrowing, and it is in English before the Conquest.
Old English mǣnan could also shade toward complaining or mourning. That second use is sometimes offered as a cousin of moan. The connection is not settled. A few dictionaries reconstruct an unrecorded Old English mānan as a variant; the Oxford English Dictionary treats moan as of uncertain origin and discounts the link. What survived as the ordinary verb is intending and signifying, not lament.
From the late fourteenth century a speaker could mean well, packing the verb with a judgment about the quality of an intention rather than its mere existence. By the late nineteenth century a person or a thing could mean a great deal in the sense of mattering. The conversational check you know what I mean is on record from the 1830s.
Shared, then low, then unkind
The unkind adjective began as a word for what people held together. Old English ġemǣne meant common, public, general, shared by all. The prefix ġe- is the same collective marker that appears across Germanic as ga-. Middle English often dropped it, leaving imene or mene. The Germanic ancestor ga-mainiz meant possessed jointly. Its further analysis is a compound: a together-prefix plus a form of the Indo-European root mei- that had to do with changing and exchanging. Latin commūnis, the source of English common, is built from comparable pieces. Common and this mean are therefore distant relatives in sense history even though they look unlike.
Cognates still show the older social meaning and, in several languages, the later sneer. Dutch gemeen and German gemein can mean common; they can also mean nasty. Gothic gamains meant common. English followed a path of rank. Around 1200 the adjective still meant shared or general, a sense now dead. By the early fourteenth century it could mark a person of low origin. Late in that century it covered ordinary skill and poor quality. The shabby, inferior reading lasted longer in American English than in Britain; nineteenth-century commentators noted mean as an Americanism for poor or shabby, applied to hotels and dinners as well as to people.
The seventeenth century added a moral turn: low-minded, without honor. Stingy is on record by the mid-eighteenth century. A milder American slang sense, disobliging or petty, appears in the nineteenth. None of those steps required a new root. They are social narrowing of a word that once named the commons.
The middle that came with French
The third mean is a loan. About 1300 English took Old French meien, a variant of moiien (modern French moyen), from Late Latin medianus, from Latin medius, in the middle, from the Indo-European root medhyo-. Median, borrowed later from the same Latin adjective, is a doublet. Nautical mizzen is another relative by that route.
The noun first shows up in music, for a tone that sits between two others. By the late fourteenth century the same stock had spread: a method or course of action, which is the ancestor of means, by means of, and by no means; the golden mean of moderation; and a physical midpoint. The mathematical average, a quantity obtained by adding values and dividing by their number, is a mid-fifteenth-century specialization. A later verb, to calculate such an average, is a nineteenth-century back-formation from the noun.
The matching adjective, occupying an intermediate place, is mid-fourteenth century. Used of people it could mean middle rank, and some of those uses may already be mixed with the native adjective of low status. Meantime and meanwhile keep the temporal middle from the fifteenth century.
When two adjectives leaned on each other
Because the native low adjective and the French middle adjective ended up identical, later English often cannot say which one a given phrase belongs to. Historical dictionaries note that some citations might be referred almost equally to either, and that mixed ancestry is likely. The praise sense, as in a musician who plays a mean solo, is recorded around 1900. It is often traced to the older understatement no mean, meaning not inferior, itself from the 1590s and already looking both at rank and at the idea of average.
The useful leftover is morphological rather than moral. The unkind mean lost a prefix that once marked joint possession. German still wears that prefix in gemein. English dropped ge-, kept the stub, and let three unrelated histories occupy one short word.