MEAN, an homonymous word, the chief uses of which may be divided thus. (1) A verb with two principal applications, to intend, purpose or design, and to signify. This word is in O.E. _maenan_, and cognate forms appear in other Teutonic languages, cf. Du. _meenen_, Ger. _meinen_. The ultimate origin is usually taken to be the root _men-_, to think, the root of "mind." (2) An adjective and substantive meaning "that which is in the middle." This is derived through the O. Fr. _men_, _meien_ or _moien_, modern _moyen_, from the late Lat. adjective _medianus_, from _medius_, middle. The law French form _mesne_ is still preserved in certain legal phrases (see MESNE). The adjective "mean" is chiefly used in the sense of "average," as in mean temperature, mean birth or death rate, &c. "Mean" as a substantive has the following principal applications; it is used of that quality, course of action, condition, state, &c., which is equally distant from two extremes, as in such phrases as the "golden (or happy) mean." For the philosophic application see ARISTOTLE and ETHICS. In mathematics, the term "mean," in its most general sense, is given to some function of two or more quantities which (1) becomes equal to each of the quantities when they themselves are made equal, and (2) is unaffected in value when the quantities suffer any transpositions. The three commonest means are the arithmetical, geometrical, and harmonic; of less importance are the contraharmonical, arithmetico-geometrical, and quadratic. From the sense of that which stands between two things, "mean," or the plural "means," often with a singular construction, takes the further significance of agency, instrument, &c., of which that produces some result, hence resources capable of producing a result, particularly the pecuniary or other resources by which a person is enabled to live, and so used either of employment or of property, wealth, &c. There are many adverbial phrases, such as "by all means," "by no means," &c., which are extensions of "means" in the sense of agency. The word "mean" (like the French _moyen_) had also the sense of middling, moderate, and this considerably influenced the uses of "mean" (3). This, which is now chiefly used in the sense of inferior, low, ignoble, or of avaricious, penurious, "stingy," meant originally that which is common to more persons or things than one. The word in O. E. is _gemaéne_, and is represented in the modern Ger. _gemein_, common. It is cognate with Lat. _communis_, from which "common" is derived. The descent in meaning from that which is shared alike by several to that which is inferior, vulgar or low, is paralleled by the uses of "common."