web.archive.org

average: Definition, Synonyms and Much More from Answers.com

️Wed Jul 01 2015

Dictionary:

average

(ăv'ər-ĭj, ăv'rĭj) pronunciation

Mathematics.
1. A number that typifies a set of numbers of which it is a function.
2. See arithmetic mean.
1. An intermediate level or degree: near the average in size.
2. The usual or ordinary kind or quality: Although the wines vary, the average is quite good.
Sports. The ratio of a team's or player's successful performances such as wins, hits, or goals, divided by total opportunities for successful performance, such as games, times at bat, or shots: finished the season with a .500 average; a batting average of .274.
Law.
1. The loss of a ship or cargo, caused by damage at sea.
2. The incurrence of damage or loss of a ship or cargo at sea.
3. The equitable distribution of such a loss among concerned parties.
4. A charge incurred through such a loss.
Nautical. Small expenses or charges that are usually paid by the master of a ship.

adj.

Mathematics. Of, relating to, or constituting an average.
Being intermediate between extremes, as on a scale: a player of average ability.
Usual or ordinary in kind or character: a poll of average people; average eyesight.
Assessed in accordance with the law of averages.

v., -aged, -ag·ing, -ag·es.

v.tr.

Mathematics. To calculate the average of: average a set of numbers.
To do or have an average of: averaged three hours of work a day.
To distribute proportionately: average one's income over four years so as to minimize the tax rate.

v.intr.

To be or amount to an average: Some sparrows are six inches long, but they average smaller. Our expenses averaged out to 45 dollars per day.

phrasal verbs:

average down

To purchase shares of the same security at successively lower prices in order to reduce the average price of one's position.

average up

To purchase shares of the same security at successively higher prices in order to achieve a larger position at an average price that is lower than the current market value.

[From Middle English averay, charge above the cost of freight, from Old French avarie, from Old Italian avaria, duty, from Arabic ‘awārīya, damaged goods, from ‘awār, blemish, from ‘awira, to be damaged.]

averagely av'er·age·ly adv.
averageness av'er·age·ness n.

SYNONYMS average, medium, mediocre, fair, middling, indifferent, tolerable. These adjectives indicate a middle position on a scale of evaluation. Average and medium apply to what is midway between extremes and imply both sufficiency and lack of distinction: a novel of average merit; an orange of medium size. Mediocre stresses the undistinguished aspect of what is average: “The caliber of the students . . . has gone from mediocre to above average” (Judy Pasternak). What is fair is passable but substantially below excellent: in fair health. Middling refers to a ranking between average and mediocre: gave a middling performance. Indifferent suggests neutrality: “His home, alas, was but an indifferent attic” (Edward Everett Hale). Something tolerable is merely acceptable: prepared a tolerable meal.

In mathematics, an average, or central tendency of a data set refers to a measure of the "middle" or "expected" value of the data set. There are many different descriptive statistics that can be chosen as a measurement of the central tendency of the data items. The most common method is the arithmetic mean, but there are more than one type of average (median being another common example).

Colloquially, people often use the term average to refer to an intuitive central tendency without having a specific measurement of central tendency in mind, or use terms such as "the average person". However, the phrase "there's no such thing as an average citizen" emphasizes that the average is a number, not a person or some other object. The average is calculated by combining the measurements related to a group of people or objects, to compute a number as being the average of the group.

Please see the table of mathematical symbols for explanations of the symbols used. In statistics, the term central tendency is used in some fields of empirical research to refer to what statisticians sometimes call "location". A "measure of central tendency" is either a location parameter or a statistic used to estimate a location parameter.

Measures of central tendency

There are many kinds of averages. The fundamental concept they have in common is that they are all ways of preserving a property of a list, which is symetric with permutations of the list, when each element of the list is replaced by the constant value of the average. For instance, that arithmetic average preserves the sum of a list when each element of the list is replaced by the arithmetic average. Thus, the arithmetic average, A, of 2 and 8 is obtained by solving: 2 + 8 = A + A. The geometric average perserves the product of a list when each element of the list is replaced by the geometric average. Thus, the geometric average, G, of 2 and 8 is obtained by solving: 2*8 = G*G. Different kinds of averages are described below.

Name	Equation or description
Arithmetic mean	$\bar{x} = \frac{1}{n}\sum_{i=1}^n x_i = \frac{1}{n} (x_1+\cdots+x_n)$
Median	The middle value that separates the higher half from the lower half of the data set
Geometric median	A rotation invariant extension of the median for points in Rⁿ
Mode	The most frequent value in the data set
Geometric mean	$\bigg(\prod_{i=1}^n x_i \bigg)^{1/n} = \sqrt[n]{x_1 \cdot x_2 \dotsb x_n}$
Harmonic mean	$\frac{n}{\frac{1}{x_1} + \frac{1}{x_2} + \cdots + \frac{1}{x_n}}$
Quadratic mean (or RMS)	$\sqrt{\frac{1}{n} \sum_{i=1}^{n} x_i^2} = \sqrt {\frac{x_1^2 + x_2^2 + \cdots + x_n^2}{n}}$
Generalized mean	$\sqrt[p]{\frac{1}{n} \cdot \sum_{i=1}^n x_{i}^p}$
Heronian mean	$\frac{2}{n(n+1)} \cdot \sum_{i=1}^n \sum_{j=1}^n \sqrt{x_i x_j}$ where j≠i
Weighted mean	$\frac{ \sum_{i=1}^n w_i x_i}{\sum_{i=1}^n w_i} = \frac{w_1 x_1 + w_2 x_2 + \cdots + w_n x_n}{w_1 + w_2 + \cdots + w_n}$
Truncated mean	The arithmetic mean of data values after a certain number or proportion of the highest and lowest data values have been discarded
Interquartile mean	A special case of the truncated mean, using the interquartile range
Midrange	$\frac{\max x + \min x}{2}$
Winsorized mean	Similar to the truncated mean, but, rather than deleting the extreme values, they are set equal to the largest and smallest values that remain
Annualization	Annualization of a set of returns is a variation on the geometric average that provides the intensive property of a return per year corresponding to a list of returns. Define the return factor as one plus the return. The annualized return factor of a list of returns is the Tth root of the product of their return factors, where T is the sum of the durations of the periods of the returns. For instance, if the return for one year is 10% and the return for a subsequent half a year is 5% then the annualized return of both of these returns together is obtained by taking the product of 1.1 and 1.05, and then taking the result to the power of one over 1.5 and then subtracting one, which gives approximately 10.08%.

Other averages

Other more sophisticated averages are: trimean, trimedian, and normalized mean. These are usually more representative of the whole data set. ^{[citation needed]}

One can create one's own average metric using generalized f-mean:

$y = f^{-1}\left(\frac{f(x_1)+f(x_2)+\cdots+f(x_n)}{n}\right),$

where f is any invertible function. The harmonic mean is an example of this using f(x) = 1/x, and the geometric mean is another, using f(x) = log x. Another example, expmean (exponential mean) is a mean using the function f(x) = e^x, and it is inherently biased towards the higher values. However, this method for generating means is not general enough to capture all averages. A more general method for defining an average, y, takes any function of a list g(x_1, x_2, ..., x_n), which is symmetric under permutation of the members of the list, and equates it to the same function with the value of the average replacing each member of the list: g(x_1, x_2, ..., x_n) = g(y, y, ..., y). This most general definition still captures the important property of all averages that the average of a list of identical elements is that element itself.

Average applied to a data stream

The concept of an average can be applied to a stream of data as well as a bounded set, the goal being to find a value about which recent data is in some way clustered. The stream may be distributed in time, as in samples taken by some data acquisition system from which we want to remove noise, or in space, as in pixels in an image from which we want to extract some property. An easy-to-understand and widely used application of average to a stream is the simple moving average in which we compute the arithmetic mean of the most recent N data items in the stream. To advance one position in the stream, we add 1/N times the new data item and subtract 1/N times the data item N places back in the stream.

Derivation of the name

The original meaning of the word average is "damage sustained at sea": the same word is found in Arabic as awar, in Italian as avaria and in French as avarie. Hence an average adjuster is a person who assesses an insurable loss.

Marine damage is either particular average, which is borne only by the owner of the damaged property, or general average, where the owner can claim a proportional contribution from all the parties to the marine venture. The type of calculations used in adjusting general average gave rise to the use of "average" to mean "arithmetic mean".

External links

Median as a weighted arithmetic mean of all Sample Observations

Calculations and comparison between arithmetic and geometric mean of two values

This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)

Dansk (Danish)
n. - gennemsnit, normal, norm
adj. - gennemsnitlig, normal, middel-
v. tr. - have som gennemsnit, udgøre gennemsnit
v. intr. - være gennemsnit, udgøre gennemsnit

idioms:

average out udlignes, jævnes
on average gennemsnitligt, i gennemsnit

Nederlands (Dutch)
gemiddeld(e), doorsnee, middelmatig, gewoon, averij (zeeschade), als gemiddelde hebben, gemiddeld per dag etc. werken/doen, het gemiddelde inschatten, kwaliteit inschatten

Français (French)
n. - moyenne, (Assur) avarie
adj. - moyenne, moyen
v. tr. - établir/faire la moyenne de, atteindre la moyenne de, (Aut) faire une moyenne de
v. intr. - s'égaliser, faire en moyenne

idioms:

average out s'égaliser, faire en moyenne
on average en moyenne

Deutsch (German)
n. - Durchschnitt, Mittelwert
adj. - durchschnittlich, Durchschnitts-, Mittel-, mittelmäßig
v. - durchschnittlich betragen, den Mittelwert nehmen

idioms:

average out sich ausgleichen
on average im Durchschnitt

Ελληνική (Greek)
n. - (μαθημ.) μέσος όρος, (ναυτ., οικον.) αβαρία, βλάβη
v. - έχω/κάνω/πιάνω/βγάζω κατά μέσον όρο, υπολογίζω/εξάγω τον μέσο όρο
adj. - μέσος, του μέσου όρου, μέτριος, αντιπροσωπευτικός, συνήθης

idioms:

average out υπολογίζω τον μέσο όρο
on average κατά μέσον όρο

Italiano (Italian)
media, medio, mediocre

idioms:

average out in media
bowling average media personale (cricket)
law of averages statistica
on average in media

Português (Portuguese)
n. - média (f), proporção (f), avaria (f)
v. - dividir proporcionalmente, calcular a média, comprar ou vender por atacado
adj. - médio, proporcional, mediano, padrão, medíocre

idioms:

average out perfazer a média
bowling average média de arremessos (Esp.)
law of averages lei das probabilidades (Mat.)
on average na média

Русский (Russian)
среднее число, средний, посредственный

idioms:

average out рассчитать среднее число
bowling average показатель в крикете
law of averages закон средних величин
on average в среднем

Español (Spanish)
n. - promedio, media, término medio, medio
adj. - regular, mediano, mediocre
v. tr. - promediar
v. intr. - hacer un promedio

idioms:

average out alcanzar un promedio de, ser por término medio
on average por término medio, como promedio, como media

Svenska (Swedish)
n. - genomsnitt, medeltal
v. - beräkna medeltalet, fördela
adj. - genomsnittlig, medel-

中文（简体） (Chinese (Simplified))
平均, 平均水平, 平均数, 一般的, 通常的, 平均的, 均分, 使平衡, 平均为

idioms:

average out 达到平均数, 最终得到平衡
on average 平均起来

中文（繁體） (Chinese (Traditional))
n. - 平均, 平均水準, 平均數
adj. - 一般的, 通常的, 平均的
v. tr. - 均分, 使平衡, 平均為
v. intr. - 平均為

idioms:

average out 達到平均數, 最終得到平衡
on average 平均起來

한국어 (Korean)
n. - 평균
adj. - 평균의, 보통의
v. tr. - 의 평균치를 구하다
v. intr. - 평균에 달하다

idioms:

average out 매매해 버리고 손을 떼다, 결국 평균치가 되다

日本語 (Japanese)
n. - 平均, 普通
v. - 平均して…になる, 平均して…を得る, 平均する
adj. - 平均の, 平均的な

idioms:

average out 結局平均…に達する
on average 平均して

العربيه (Arabic)
‏(الاسم) معدل, متوسط, عادي (فعل) يوجد المعدل, يقسم على نحو متناسب (صفه) يعمل بمعدل, يبلغ معدله‏

עברית (Hebrew)
n. - ‮ממוצע‬
adj. - ‮ממוצע, רגיל, בינוני‬
v. tr. - ‮חישב את הממוצע, מיצע, העריך את הרמה הכללית או את הממוצע של‬
v. intr. - ‮הציג את הממוצע של‬

If you are unable to view some languages clearly, click here.

To select your translation preferences click here.