Mean
Mean
men: The noun meaning (Dan 8:15 the King James Version, the Revised Version (British and American) I sought to understand; and 1Co 14:11) is synonymous with signification but in 1 Macc 15:4 the King James Version it expresses purpose (the Revised Version (British and American) I am minded to land). The noun mean in Hebrew always occurs in the plural, and is generally used in the sense of agency, instrument (compare 1Ki 10:29, etc.). the Revised Version (British and American) very frequently changes, King James Version: The Wisdom of Solomon 8:13, because of her; 2Th 2:3, in any wise; Luk 8:36, how; Pro 6:26, on account of; Rev 13:14, by reason of (compare also 2Th 3:16; Joh 9:21). Heb 9:15 (the King James Version that by means of death) translates literally, that a death having taken place, from , gnomai, to become, to happen. Act 18:21 the King James Version, I must by all means keep this feast, is omitted in the Revised Version (British and American) in harmony with several cursives, the Vulgate, and some other versions
The adjective mean is used in the sense of common, humble (, ‘adham, man; compare Isa 2:9; Isa 5:15; Isa 31:8 omits mean). It is also used in the sense of obscure (Pro 22:29, , hashokh, obscure; , asemos, literally, without a mark, unknown, Act 21:39). Mean is found in expressions like in the meanwhile (the King James Version 1Ki 18:45, the Revised Version (British and American) little while; Joh 4:31; Rom 2:15, the Revised Version (British and American) one with another); in the meantime (1 Macc 11:41 the King James Version; Luk 12:1); and in the mean season the King James Version (1 Macc 11:14; 15:15). The adverb meanly is found (2 Macc 15:38) in the sense of moderately.
The verb mean expresses purpose (Isa 3:15; Isa 10:7; Gen 50:20, etc.). In some cases the Revised Version (British and American) renders literal translation: Act 27:2, was about to sail (the King James Version meaning to sail); compare Act 21:13; 2Co 8:13. In other instances the idea of to mean is to signify, to denote (1Sa 4:6; Gen 21:29; Mat 9:13, etc.). Luk 15:26 translates literally, what these things might be. In Exo 12:26 the sense of mean ye is to have in mind.
Fuente: International Standard Bible Encyclopedia
Mean
In general, that which in some way mediates or occupies a middle position among various things or between two extremes. Hence (especially in the plural) that through which an end is attained; in mathematics the word is used for any one of various notions of average; in ethics it represents moderation, temperance, prudence, the middle way.
In mathematics
The arithmetic mean of two quantities is half their sum; the arithmetic mean of n quantities is the sum of the n quantities, divided by n. In the case of a function f(x) (say from real numbers to real numbers) the mean value of the function for the values x1, x2, . . . , xn of x is the arithmetic mean of f(x1), f(x2), . . . , f(xn). This notion is extended to the case of infinite sets of values of x by means of integration; thus the mean value of f(x) for values of x between a and b is ?f(x)dx, with a and b as the limits of integration, divided by the difference between a and b.
The geometric mean of or between, or the mean proportional between, two quantities is the (positive) square root of their product. Thus if b is the geometric mean between a and c, c is as many times greater (or less) than b as b is than a. The geometric mean of n quantities is the nth root of their product.
The harmonic mean of two quantities is defined as the reciprocal of the arithmetic mean of their reciprocals. Hence the harmonic mean of a and b is 2ab/(a + b).
The weighted mean or weighted average of a set of n quantities, each of which is associated with a certain number as weight, is obtained by multiplying each quantity by the associated weight, adding these products together, and then dividing by the sum of the weights. As under A, this may be extended to the case of an infinite set of quantities by means of integration. (The weights have the role of estimates of relative importance of the various quantities, and if all the weights are equal the weighted mean reduces to the simple arithmetic mean.)
In statistics, given a population (i.e., an aggregate of observed or observable quantities) and a variable x having the population as its range, we have
The mean value of x is the weighted mean of the values of x, with the probability (frequency ratio) of each value taken as its weight. In the case of a finite population this is the same as the simple arithmetic mean of the population, provided that, in calculating the arithmetic mean, each value of x is counted as many times over as it occurs in the set of observations constituting the population.
In like manner, the mean value of a function f(x) of x is the weighted mean of the values of f(x), where the probability of each value of x is taken as the weight of the corresponding value of f(x).
The mode of the population is the most probable (most frequent) value of x, provided there is one such.
The median of the population is so chosen that the probability that x be less than the median (or the probability that x be greater than the median) is (or as near as possible). In the case of a finite population, if the values of x are arranged in order of magnitude — repeating any one value of x as many times over as it occurs in the set of observations constituting the population — then the middle term of this series, or the arithmetic mean of the two middle terms, is the median. — A.C.
In cosmology, the fundamental means (arithmetic, geometric, and harmonic) were used by the Greeks in describing or actualizing the process of becoming in nature. The Pythagoreans and the Platonists in particular made considerable use of these means (see the Philebus and the Timaeus more especially). These ratios are among the basic elements used by Plato in his doctrine of the mixtures. With the appearance of the qualitative physics of Aristotle, the means lost their cosmological importance and were thereafter used chiefly in mathematics. The modern mathematical theories of the universe make use of the whole range of means analyzed by the calculus of probability, the theory of errors, the calculus of variations, and the statistical methods.
In ethics, the ‘Doctrine of the Mean’ is the moral theory of moderation, the development of the virtues, the determination of the wise course in action, the practice of temperance and prudence, the choice of the middle way between extreme or conflicting decisions. It has been developed principally by the Chinese, the Indians and the Greeks; it was used with caution by the Christian moralists on account of their rigorous application of the moral law.
In Chinese philosophy, the Doctrine of the Mean or of the Middle Way (the Chung Yung, literally ‘Equilibrium and Harmony’) involves the absence of immoderate pleasure, anger, sorrow or joy, and a conscious state in which those feelings have been stirred and act in their proper degree. This doctrine has been developed by Tzu Shu (V. C. B.C.), a grandson of Confucius who had already described the virtues of the ‘superior man’ according to his aphorism “Perfect is the virtue which is according to the mean”. In matters of action, the superior man stands erect in the middle and strives to follow a course which does not incline on either side.
In Buddhist philosophy, the System of the Middle Way or Madhyamaka is ascribed more particularly to Nagarjuna (II c. A.D.). The Buddha had given his revelation as a mean or middle way, because he repudiated the two extremes of an exaggerated ascetlsm and of an easy secular life. This principle is also applied to knowledge and action in general, with the purpose of striking a happy medium between contradictory judgments and motives. The final objective is the realization of the nirvana or the complete absence of desire by the gradual destruction of feelings and thoughts. But while orthodox Buddhism teaches the unreality of the individual (who is merely a mass of causes and effects following one another in unbroken succession), the Madhyamaka denies also the existence of these causes and effects in themselves. For this system, “Everything is void”, with the legitimate conclusion that “Absolute truth is silence”. Thus the perfect mean is realized.
In Greek Ethics, the doctrine of the Right (Mean has been developed by Plato (Philebus) and Aristotle (Nic. Ethics II. 6-8) principally, on the Pythagorean analogy between the sound mind, the healthy body and the tuned string, which has inspired most of the Greek Moralists. Though it is known as the “Aristotelian Principle of the Mean”, it is essentially a Platonic doctrine which is preformed in the Republic and the Statesman and expounded in the Philebus, where we are told that all good things in life belong to the class of the mixed (26 D). This doctrine states that in the application of intelligence to any kind of activity, the supreme wisdom is to know just where to stop, and to stop just there and nowhere else. Hence, the “right-mean” does not concern the quantitative measurement of magnitudes, but simply the qualitative comparison of values with respect to a standard which is the appropriate (prepon), the seasonable (kairos), the morally necessary (deon), or generally the moderate (metrion). The difference between these two kinds of metretics (metretike) is that the former is extrinsic and relative, while the latter is intrinsic and absolute. This explains the Platonic division of the sciences into two classesthose involving reference to relative quantities (mathematical or natural), and those requiring absolute values (ethics and aesthetics). The Aristotelian analysis of the “right mean” considers moral goodness as a fixed and habitual proportion in our appetitions and tempers, which can be reached by training them until they exhibit just the balance required by the right rule. This process of becoming good develops certain habits of virtues consisting in reasonable moderation where both excess and defect are avoidedthe virtue of temperance (sophrosyne) is a typical example. In this sense, virtue occupies a middle position between extremes, and is said to be a mean; but it is not a static notion, as it leads to the development of a stable being, when man learns not to over-reach himself. This qualitative conception of the mean involves an adaptation of the agent, his conduct and his environment, similar to the harmony displayed in a work of art. Hence the aesthetic aspect of virtue, which is often overstressed by ancient and neo-pagan writers, at the expense of morality proper.
The ethical idea of the mean, stripped of the qualifications added to it by its Christian interpreters, has influenced many positivistic systems of ethics, and especially pragmatism and behaviourism (e.g., A. Huxley’s rule of Balanced Excesses). It is maintained that it is also involved in the dialectical systems, such as Hegelianism, where it would have an application in the whole dialectical process as suchthus, it would correspond to the synthetic phase which blends together the thesis and the antithesis by the meeting of the opposites.
— T.G.