 mean

mean^{1}
v.t.1. to have in mind as one's purpose or intention; intend: I meant to compliment you on your work.2. to intend for a particular purpose, destination, etc.: They were meant for each other.3. to intend to express or indicate: What do you mean by "liberal"?4. to have as its sense or signification; signify: The word "freedom" means many things to many people.5. to bring, cause, or produce as a result: This bonus means that we can take a trip to Florida.6. to have (certain intentions) toward a person: He didn't mean you any harm.7. to have the value of; assume the importance of: Money means everything to them. She means the world to him.v.i.8. to be minded or disposed; have intentions: Beware, she means ill, despite her solicitous manner.9. mean well, to have good intentions; try to be kind or helpful: Her constant queries about your health must be tiresome, but I'm sure she means well.[bef. 900; ME menen, OE maenan; c. G meinen, D meenen]Syn. 1. contemplate. See intend. 2. destine, foreordain. 4. denote, indicate; import, imply, connote.mean^{2}/meen/, adj., meaner, meanest.1. offensive, selfish, or unaccommodating; nasty; malicious: a mean remark; He gets mean when he doesn't get his way.2. smallminded or ignoble: mean motives.3. penurious, stingy, or miserly: a person who is mean about money.4. inferior in grade, quality, or character: no mean reward.5. low in status, rank, or dignity: mean servitors.6. of little importance or consequence: mean little details.7. unimposing or shabby: a mean abode.8. small, humiliated, or ashamed: You should feel mean for being so stingy.9. Informal. in poor physical condition.10. troublesome or vicious; badtempered: a mean old horse.11. Slang. skillful or impressive: He blows a mean trumpet.[bef. 900; ME mene, aph. var. (see Y) of imene, OE gemaene; c. D gemeen, G gemein common, Goth gamains in common; cf. COMMON]Syn. 2. contemptible, despicable. MEAN, LOW, BASE, SORDID, and VILE all refer to ignoble characteristics worthy of dislike, contempt, or disgust. MEAN suggests pettiness and smallmindedness: to take a mean advantage. LOW suggests coarseness and vulgarity: low company. BASE suggests selfish cowardice or moral depravity: base motives.SORDID suggests a wretched uncleanness, or sometimes an avariciousness without dignity or moral scruples: a sordid slum; sordid gain. VILE suggests disgusting foulness or repulsiveness: vile insinuation; a vile creature. 3. niggardly, close, tight, parsimonious, illiberal, ungenerous, selfish. See stingy. 5. common, humble; undignified, plebeian. 6. inconsequential, insignificant, petty, paltry, little, poor, wretched. 7. squalid, poor.mean^{3}/meen/, n.1. Usually, means. (used with a sing. or pl. v.) an agency, instrument, or method used to attain an end: The telephone is a means of communication. There are several means of solving the problem.2. means,a. available resources, esp. money: They lived beyond their means.b. considerable financial resources; riches: a man of means.3. something that is midway between two extremes; something intermediate: to seek a mean between cynicism and blind faith.4. Math.a. a quantity having a value intermediate between the values of other quantities; an average, esp. the arithmetic mean.b. either the second or third term in a proportion of four terms.6. Logic. the middle term in a syllogism.7. by all means,a. (in emphasis) certainly: Go, by all means.b. at any cost; without fail.8. by any means, in any way; at all: We were not surprised at the news by any means.9. by means of, with the help of; by the agency of; through: We crossed the stream by means of a log.10. by no means, in no way; not at all: The prize is by no means certain.adj.11. occupying a middle position or an intermediate place, as in kind, quality, degree, or time: a mean speed; a mean course; the mean annual rainfall.[130050; ME mene < MF meen, var. of meien < L medianus; see MEDIAN]
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(as used in expressions)Doctrine of the Meanmean median and modemean value theorems* * *
in mathematics, a quantity that has a value intermediate between those of the extreme members of some set. Several kinds of mean exist, and the method of calculating a mean depends upon the relationship known or assumed to govern the other members. The arithmetic mean, denoted x, of a set of n numbers x_{1}, x_{2}, …, x_{n} is defined as the sum of the numbers divided by n:The arithmetic mean (usually synonymous with average) represents a point about which the numbers balance. For example, if unit masses are placed on a line at points with coordinates x_{1}, x_{2}, …, x_{n}, then the arithmetic mean is the coordinate of the centre of gravity of the system. In statistics, the arithmetic mean is commonly used as the single value typical of a set of data. For a system of particles having unequal masses, the centre of gravity is determined by a more general average, the weighted arithmetic mean. If each number (x) is assigned a corresponding positive weight (w), the weighted arithmetic mean is defined as the sum of their products (wx) divided by the sum of their weights. In this case,The weighted arithmetic mean also is used in statistical analysis of grouped data: each number x_{i} is the midpoint of an interval, and each corresponding value of w_{i} is the number of data points within that interval.For a given set of data, many possible means can be defined, depending on which features of the data are of interest. For example, suppose five squares are given, with sides 1, 1, 2, 5, and 7 cm. Their average area is (1^{2} + 1^{2} + 2^{2} + 5^{2} + 7^{2})/5, or 16 square cm, the area of a square of side 4 cm. The number 4 is the quadratic mean (or root mean square) of the numbers 1, 1, 2, 5, and 7 and differs from their arithmetic mean, which is 3 ^{1}/_{5}. In general, the quadratic mean of n numbers x_{1}, x_{2}, …, x_{n} is the square root of the arithmetic mean of their squares,The arithmetic mean gives no indication of how widely the data are spread or dispersed about the mean. Measures of the dispersion are provided by the arithmetic and quadratic means of the n differences x_{1} − x, x_{2} − x, …, x_{n} − x. The quadratic mean gives the “standard deviation” of x_{1}, x_{2}, …, x_{n}.The arithmetic and quadratic means are the special cases p = 1 and p = 2 of the pthpower mean, M_{p}, defined by the formulawhere p may be any real number except zero. The case p = −1 is also called the harmonic mean. Weighted pthpower means are defined byIf x is the arithmetic mean of x_{1} and x_{2}, the three numbers x_{1}, x, x_{2} are in arithmetic progression. If h is the harmonic mean of x_{1} and x_{2}, the numbers x_{1}, h, x_{2} are in harmonic progression. A number g such that x_{1}, g, x_{2} are in geometric progression is defined by the condition that x_{1}/g = g/x_{2}, or g^{2} = x_{1}x_{2}; henceThis g is called the geometric mean of x_{1} and x_{2}. The geometric mean of n numbers x_{1}, x_{2}, …, x_{n} is defined to be the nth root of their product:All the means discussed are special cases of a more general mean. If f is a function having an inverse f ^{−1} (a function that “undoes” the original function), the numberis called the mean value of x_{1}, x_{2}, …, x_{n} associated with f. When f(x) = x^{p}, the inverse is f ^{−1}(x) = x^{1/p}, and the mean value is the pthpower mean, M_{p}. When f(x) = ln x (the natural logarithm), the inverse is f ^{−1}(x) = e^{x} (the exponential function), and the mean value is the geometric mean.For information on the development of various definitions of the mean, see probability and statistics. For further technical information, see statistics and probability theory.* * *
Universalium. 2010.