The word average means - Word и Excel - помощь в работе с программами

From Wikipedia, the free encyclopedia

In ordinary language, an average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list (the arithmetic mean). For example, the average of the numbers 2, 3, 4, 7, and 9 (summing to 25) is 5. Depending on the context, an average might be another statistic such as the median, or mode. For example, the average personal income is often given as the median—the number below which are 50% of personal incomes and above which are 50% of personal incomes—because the mean would be higher by including personal incomes from a few billionaires. For this reason, it is recommended to avoid using the word «average» when discussing measures of central tendency.

General properties[edit]

If all numbers in a list are the same number, then their average is also equal to this number. This property is shared by each of the many types of average.

Another universal property is monotonicity: if two lists of numbers A and B have the same length, and each entry of list A is at least as large as the corresponding entry on list B, then the average of list A is at least that of list B. Also, all averages satisfy linear homogeneity: if all numbers of a list are multiplied by the same positive number, then its average changes by the same factor.

In some types of average, the items in the list are assigned different weights before the average is determined. These include the weighted arithmetic mean, the weighted geometric mean and the weighted median. Also, for some types of moving average, the weight of an item depends on its position in the list. Most types of average, however, satisfy permutation-insensitivity: all items count equally in determining their average value and their positions in the list are irrelevant; the average of (1, 2, 3, 4, 6) is the same as that of (3, 2, 6, 4, 1).

Pythagorean means[edit]

The arithmetic mean, the geometric mean and the harmonic mean are known collectively as the Pythagorean means.

Statistical location[edit]

The mode, the median, and the mid-range are often used in addition to the mean as estimates of central tendency in descriptive statistics. These can all be seen as minimizing variation by some measure; see Central tendency § Solutions to variational problems.

Comparison of common averages of values { 1, 2, 2, 3, 4, 7, 9 }

Type	Description	Example	Result
Arithmetic mean	Sum of values of a data set divided by number of values: $scriptstyle {bar {x}}={frac {1}{n}}sum _{{i=1}}^{n}x_{i}$	(1+2+2+3+4+7+9) / 7	4
Median	Middle value separating the greater and lesser halves of a data set	1, 2, 2, 3, 4, 7, 9	3
Mode	Most frequent value in a data set	1, 2, 2, 3, 4, 7, 9	2
Mid-range	The arithmetic mean of the highest and lowest values of a set	(1+9) / 2	5

Mode[edit]

The most frequently occurring number in a list is called the mode. For example, the mode of the list (1, 2, 2, 3, 3, 3, 4) is 3. It may happen that there are two or more numbers which occur equally often and more often than any other number. In this case there is no agreed definition of mode. Some authors say they are all modes and some say there is no mode.

Median[edit]

The median is the middle number of the group when they are ranked in order. (If there are an even number of numbers, the mean of the middle two is taken.)

Thus to find the median, order the list according to its elements’ magnitude and then repeatedly remove the pair consisting of the highest and lowest values until either one or two values are left. If exactly one value is left, it is the median; if two values, the median is the arithmetic mean of these two. This method takes the list 1, 7, 3, 13 and orders it to read 1, 3, 7, 13. Then the 1 and 13 are removed to obtain the list 3, 7. Since there are two elements in this remaining list, the median is their arithmetic mean, (3 + 7)/2 = 5.

Mid-range[edit]

The mid-range is the arithmetic mean of the highest and lowest values of a set.

Summary of types[edit]

Name	Equation or description	As solution to optimization problem
Arithmetic mean	$bar{x} = frac{1}{n}sum_{i=1}^n x_i = frac{1}{n} (x_1 + cdots + x_n)$	${displaystyle {underset {xin mathbb {R} }{operatorname {argmin} }},sum _{i=1}^{n}(x-x_{i})^{2}}$
Median	The middle value that separates the higher half from the lower half of the data set	${displaystyle {underset {xin mathbb {R} }{operatorname {argmin} }},sum _{i=1}^{n}\|x-x_{i}\|}$
Geometric median	A rotation invariant extension of the median for points in $mathbb {R} ^{d}$	${displaystyle {underset {{vec {x}}in mathbb {R} ^{d}}{operatorname {argmin} }},sum _{i=1}^{n}\|\|{vec {x}}-{vec {x}}_{i}\|\|_{2}}$
Tukey median	Another rotation invariant extension of the median for points in $mathbb {R} ^{d}$ —a point that maximizes the Tukey depth	${displaystyle {underset {{vec {x}}in mathbb {R} ^{d}}{operatorname {argmax} }},{underset {{vec {u}}in mathbb {R} ^{d}}{operatorname {min} }},sum _{i=1}^{n}left({begin{cases}1,{text{ if }}({vec {x}}_{i}-{vec {x}})cdot {vec {u}}geq 0\0,{text{ otherwise}}end{cases}}right)}$
Mode	The most frequent value in the data set	${displaystyle {underset {xin mathbb {R} }{operatorname {argmax} }},sum _{i=1}^{n}left({begin{cases}1,{text{ if }}x=x_{i}\0,{text{ if }}xneq x_{i}end{cases}}right)}$
Geometric mean	${displaystyle {sqrt[{n}]{prod _{i=1}^{n}x_{i}}}={sqrt[{n}]{x_{1}cdot x_{2}dotsb x_{n}}}}$	${displaystyle {underset {xin mathbb {R} _{>0}}{operatorname {argmin} }},sum _{i=1}^{n}(ln(x)-ln(x_{i}))^{2},qquad {text{if }}x_{i}>0,forall ,iin {1,dots ,n}}$
Harmonic mean	$frac{n}{frac{1}{x_1} + frac{1}{x_2} + cdots + frac{1}{x_n}}$	${displaystyle {underset {xin mathbb {R} _{neq 0}}{operatorname {argmin} }},sum _{i=1}^{n}left({frac {1}{x}}-{frac {1}{x_{i}}}right)^{2}}$
Lehmer mean	${displaystyle {frac {sum _{i=1}^{n}x_{i}^{p}}{sum _{i=1}^{n}x_{i}^{p-1}}}}$
Quadratic mean (or RMS)	$sqrt{frac{1}{n} sum_{i=1}^{n} x_i^2} = sqrt{frac{1}{n}left(x_1^2 + x_2^2 + cdots + x_n^2right)}$	${displaystyle {underset {xin mathbb {R} _{geq 0}}{operatorname {argmin} }},sum _{i=1}^{n}(x^{2}-x_{i}^{2})^{2}}$
Cubic mean	${sqrt[ {3}]{{frac {1}{n}}sum _{{i=1}}^{{n}}x_{i}^{3}}}={sqrt[ {3}]{{frac {1}{n}}left(x_{1}^{3}+x_{2}^{3}+cdots +x_{n}^{3}right)}}$	${displaystyle {underset {xin mathbb {R} _{geq 0}}{operatorname {argmin} }},sum _{i=1}^{n}(x^{3}-x_{i}^{3})^{2},qquad {text{if }}x_{i}geq 0,forall ,iin {1,dots ,n}}$
Generalized mean	$sqrt[p]{frac{1}{n} cdot sum_{i=1}^n x_{i}^p}$	${displaystyle {underset {xin mathbb {R} _{geq 0}}{operatorname {argmin} }},sum _{i=1}^{n}(x^{p}-x_{i}^{p})^{2},qquad {text{if }}x_{i}geq 0,forall ,iin {1,dots ,n}}$
Quasi-arithmetic mean	${displaystyle f^{-1}left({frac {1}{n}}sum _{k=1}^{n}f(x_{k})right)}$	${displaystyle {underset {xin operatorname {dom} (f)}{operatorname {argmin} }},sum _{i=1}^{n}(f(x)-f(x_{i}))^{2},qquad {text{if }}f}$ is monotonic
Weighted mean	$frac{ sum_{i=1}^n w_i x_i}{sum_{i=1}^n w_i} = frac{w_1 x_1 + w_2 x_2 + cdots + w_n x_n}{w_1 + w_2 + cdots + w_n}$	${displaystyle {underset {xin mathbb {R} }{operatorname {argmin} }},sum _{i=1}^{n}w_{i}(x-x_{i})^{2}}$
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. A special case of the inter-quantile truncated mean, which operates on quantiles (often deciles or percentiles) that are equidistant but on opposite sides of the median.
Midrange	$frac{1}{2}left(max x + min xright)$	${displaystyle {underset {xin mathbb {R} }{operatorname {argmin} }},{underset {iin {1,dots ,n}}{operatorname {max} }},\|x-x_{i}\|}$
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

The table of mathematical symbols explains the symbols used below.

Miscellaneous types[edit]

Other more sophisticated averages are: trimean, trimedian, and normalized mean, with their generalizations.^[1]

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

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

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.

However, this method for generating means is not general enough to capture all averages. A more general method^[2]^{[failed verification]} for defining an average takes any function g(x₁, x₂, …, x_n) of a list of arguments that is continuous, strictly increasing in each argument, and symmetric (invariant under permutation of the arguments). The average y is then the value that, when replacing each member of the list, results in the same function value: g(y, y, …, y) = g(x₁, x₂, …, x_n). 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. The function g(x₁, x₂, …, x_n) = x₁+x₂+ ··· + x_n provides the arithmetic mean. The function g(x₁, x₂, …, x_n) = x₁x₂···x_n (where the list elements are positive numbers) provides the geometric mean. The function g(x₁, x₂, …, x_n) = (x₁⁻¹+x₂⁻¹+ ··· + x_n⁻¹)⁻¹) (where the list elements are positive numbers) provides the harmonic mean.^[2]

Average percentage return and CAGR[edit]

A type of average used in finance is the average percentage return. It is an example of a geometric mean. When the returns are annual, it is called the Compound Annual Growth Rate (CAGR). For example, if we are considering a period of two years, and the investment return in the first year is −10% and the return in the second year is +60%, then the average percentage return or CAGR, R, can be obtained by solving the equation: (1 − 10%) × (1 + 60%) = (1 − 0.1) × (1 + 0.6) = (1 + R) × (1 + R). The value of R that makes this equation true is 0.2, or 20%. This means that the total return over the 2-year period is the same as if there had been 20% growth each year. The order of the years makes no difference – the average percentage returns of +60% and −10% is the same result as that for −10% and +60%.

This method can be generalized to examples in which the periods are not equal. For example, consider a period of a half of a year for which the return is −23% and a period of two and a half years for which the return is +13%. The average percentage return for the combined period is the single year return, R, that is the solution of the following equation: (1 − 0.23)^0.5 × (1 + 0.13)^2.5 = (1 + R)^0.5+2.5, giving an average return R of 0.0600 or 6.00%.

Moving average[edit]

Given a time series, such as daily stock market prices or yearly temperatures, people often want to create a smoother series.^[3] This helps to show underlying trends or perhaps periodic behavior. An easy way to do this is the moving average: one chooses a number n and creates a new series by taking the arithmetic mean of the first n values, then moving forward one place by dropping the oldest value and introducing a new value at the other end of the list, and so on. This is the simplest form of moving average. More complicated forms involve using a weighted average. The weighting can be used to enhance or suppress various periodic behavior and there is very extensive analysis of what weightings to use in the literature on filtering. In digital signal processing the term «moving average» is used even when the sum of the weights is not 1.0 (so the output series is a scaled version of the averages).^[4] The reason for this is that the analyst is usually interested only in the trend or the periodic behavior.

History[edit]

Origin[edit]

The first recorded time that the arithmetic mean was extended from 2 to n cases for the use of estimation was in the sixteenth century. From the late sixteenth century onwards, it gradually became a common method to use for reducing errors of measurement in various areas.^[5]^[6] At the time, astronomers wanted to know a real value from noisy measurement, such as the position of a planet or the diameter of the moon. Using the mean of several measured values, scientists assumed that the errors add up to a relatively small number when compared to the total of all measured values. The method of taking the mean for reducing observation errors was indeed mainly developed in astronomy.^[5]^[7] A possible precursor to the arithmetic mean is the mid-range (the mean of the two extreme values), used for example in Arabian astronomy of the ninth to eleventh centuries, but also in metallurgy and navigation.^[6]

However, there are various older vague references to the use of the arithmetic mean (which are not as clear, but might reasonably have to do with our modern definition of the mean). In a text from the 4th century, it was written that (text in square brackets is a possible missing text that might clarify the meaning):^[8]

In the first place, we must set out in a row the sequence of numbers from the monad up to nine: 1, 2, 3, 4, 5, 6, 7, 8, 9. Then we must add up the amount of all of them together, and since the row contains nine terms, we must look for the ninth part of the total to see if it is already naturally present among the numbers in the row; and we will find that the property of being [one] ninth [of the sum] only belongs to the [arithmetic] mean itself…

Even older potential references exist. There are records that from about 700 BC, merchants and shippers agreed that damage to the cargo and ship (their «contribution» in case of damage by the sea) should be shared equally among themselves.^[7] This might have been calculated using the average, although there seem to be no direct record of the calculation.

Etymology[edit]

The root is found in Arabic as عوار ʿawār, a defect, or anything defective or damaged, including partially spoiled merchandise; and عواري ʿawārī (also عوارة ʿawāra) = «of or relating to ʿawār, a state of partial damage».^[9] Within the Western languages the word’s history begins in medieval sea-commerce on the Mediterranean. 12th and 13th century Genoa Latin avaria meant «damage, loss and non-normal expenses arising in connection with a merchant sea voyage»; and the same meaning for avaria is in Marseille in 1210, Barcelona in 1258 and Florence in the late 13th.^[10] 15th-century French avarie had the same meaning, and it begot English «averay» (1491) and English «average» (1502) with the same meaning. Today, Italian avaria, Catalan avaria and French avarie still have the primary meaning of «damage». The huge transformation of the meaning in English began with the practice in later medieval and early modern Western merchant-marine law contracts under which if the ship met a bad storm and some of the goods had to be thrown overboard to make the ship lighter and safer, then all merchants whose goods were on the ship were to suffer proportionately (and not whoever’s goods were thrown overboard); and more generally there was to be proportionate distribution of any avaria. From there the word was adopted by British insurers, creditors, and merchants for talking about their losses as being spread across their whole portfolio of assets and having a mean proportion. Today’s meaning developed out of that, and started in the mid-18th century, and started in English.^[10] [1].

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».

A second English usage, documented as early as 1674 and sometimes spelled «averish», is as the residue and second growth of field crops, which were considered suited to consumption by draught animals («avers»).^[11]

There is earlier (from at least the 11th century), unrelated use of the word. It appears to be an old legal term for a tenant’s day labour obligation to a sheriff, probably anglicised from «avera» found in the English Domesday Book (1085).

The Oxford English Dictionary, however, says that derivations from German hafen haven, and Arabic ʿawâr loss, damage, have been «quite disposed of» and the word has a Romance origin.^[12]

Averages as a rhetorical tool[edit]

Due to the aforementioned colloquial nature of the term «average», the term can be used to obfuscate the true meaning of data and suggest varying answers to questions based on the averaging method (most frequently arithmetic mean, median, or mode) used. In his article «Framed for Lying: Statistics as In/Artistic Proof», University of Pittsburgh faculty member Daniel Libertz comments that statistical information is frequently dismissed from rhetorical arguments for this reason.^[13] However, due to their persuasive power, averages and other statistical values should not be discarded completely, but instead used and interpreted with caution. Libertz invites us to engage critically not only with statistical information such as averages, but also with the language used to describe the data and its uses, saying: «If statistics rely on interpretation, rhetors should invite their audience to interpret rather than insist on an interpretation.»^[13] In many cases, data and specific calculations are provided to help facilitate this audience-based interpretation.

References[edit]

^ Merigo, Jose M.; Cananovas, Montserrat (2009). «The Generalized Hybrid Averaging Operator and its Application in Decision Making». Journal of Quantitative Methods for Economics and Business Administration. 9: 69–84. ISSN 1886-516X.^{[permanent dead link]}
^ ^a ^b Bibby, John (1974). «Axiomatisations of the average and a further generalisation of monotonic sequences». Glasgow Mathematical Journal. 15: 63–65. doi:10.1017/s0017089500002135.
^ Box, George E.P.; Jenkins, Gwilym M. (1976). Time Series Analysis: Forecasting and Control (revised ed.). Holden-Day. ISBN 0816211043.
^ Haykin, Simon (1986). Adaptive Filter Theory. Prentice-Hall. ISBN 0130040525.
^ ^a ^b Plackett, R. L. (1958). «Studies in the History of Probability and Statistics: VII. The Principle of the Arithmetic Mean». Biometrika. 45 (1/2): 130–135. doi:10.2307/2333051. JSTOR 2333051.
^ ^a ^b Eisenhart, Churchill. «The development of the concept of the best mean of a set of measurements from antiquity to the present day.» Unpublished presidential address, American Statistical Association, 131st Annual Meeting, Fort Collins, Colorado. 1971.
^ ^a ^b Bakker, Arthur. «The early history of average values and implications for education.» Journal of Statistics Education 11.1 (2003): 17-26.
^ «Waterfield, Robin. «The theology of arithmetic.» On the Mystical, mathematical and Cosmological Symbolism of the First Ten Number (1988). page 70″ (PDF). Archived from the original (PDF) on 2016-03-04. Retrieved 2018-11-27.
^ Medieval Arabic had عور ʿawr meaning «blind in one eye» and عوار ʿawār meant «any defect, or anything defective or damaged». Some medieval Arabic dictionaries are at Baheth.info Archived 2013-10-29 at the Wayback Machine, and some translation to English of what’s in the medieval Arabic dictionaries is in Lane’s Arabic-English Lexicon, pages 2193 and 2195. The medieval dictionaries do not list the word-form عوارية ʿawārīa. ʿAwārīa can be naturally formed in Arabic grammar to refer to things that have ʿawār, but in practice in medieval Arabic texts ʿawārīa is a rarity or non-existent, while the forms عواري ʿawārī and عوارة ʿawāra are frequently used when referring to things that have ʿawār or damage – this can be seen in the searchable collection of medieval texts at AlWaraq.net (book links are clickable on righthand side).
^ ^a ^b The Arabic origin of avaria was first reported by Reinhart Dozy in the 19th century. Dozy’s original summary is in his 1869 book Glossaire. Summary information about the word’s early records in Italian-Latin, Italian, Catalan, and French is at avarie @ CNRTL.fr Archived 2019-01-06 at the Wayback Machine. The seaport of Genoa is the location of the earliest-known record in European languages, year 1157. A set of medieval Latin records of avaria at Genoa is in the downloadable lexicon Vocabolario Ligure, by Sergio Aprosio, year 2001, avaria in Volume 1 pages 115-116. Many more records in medieval Latin at Genoa are at StoriaPatriaGenova.it, usually in the plurals avariis and avarias. At the port of Marseille in the 1st half of the 13th century notarized commercial contracts have dozens of instances of Latin avariis (ablative plural of avaria), as published in Blancard year 1884. Some information about the English word over the centuries is at NED (year 1888). See also the definition of English «average» in English dictionaries published in the early 18th century, i.e., in the time period just before the big transformation of the meaning: Kersey-Phillips’ dictionary (1706), Blount’s dictionary (1707 edition), Hatton’s dictionary (1712), Bailey’s dictionary (1726), Martin’s dictionary (1749). Some complexities surrounding the English word’s history are discussed in Hensleigh Wedgwood year 1882 page 11 and Walter Skeat year 1888 page 781. Today there is consensus that: (#1) today’s English «average» descends from medieval Italian avaria, Catalan avaria, and (#2) among the Latins the word avaria started in the 12th century and it started as a term of Mediterranean sea-commerce, and (#3) there is no root for avaria to be found in Latin, and (#4) a substantial number of Arabic words entered Italian, Catalan and Provençal in the 12th and 13th centuries starting as terms of Mediterranean sea-commerce, and (#5) the Arabic ʿawār | ʿawārī is phonetically a good match for avaria, as conversion of w to v was regular in Latin and Italian, and -ia is a suffix in Italian, and the Western word’s earliest records are in Italian-speaking locales (writing in Latin). And most commentators agree that (#6) the Arabic ʿawār | ʿawārī = «damage | relating to damage» is semantically a good match for avaria = «damage or damage expenses». A minority of commentators have been dubious about this on the grounds that the early records of Italian-Latin avaria have, in some cases, a meaning of «an expense» in a more general sense – see TLIO (in Italian). The majority view is that the meaning of «an expense» was an expansion from «damage and damage expense», and the chronological order of the meanings in the records supports this view, and the broad meaning «an expense» was never the most commonly used meaning. On the basis of the above points, the inferential step is made that the Latinate word came or probably came from the Arabic word.
^ Ray, John (1674). A Collection of English Words Not Generally Used. London: H. Bruges. Retrieved 18 May 2015.
^ «average, n.2». OED Online. September 2019. Oxford University Press. https://www.oed.com/view/Entry/13681 (accessed September 05, 2019).
^ ^a ^b Libertz, Daniel (2018-12-31). «Framed for Lying: Statistics as In/Artistic Proof». Res Rhetorica. 5 (4). doi:10.29107/rr2018.4.1. ISSN 2392-3113.

External links[edit]

Look up average in Wiktionary, the free dictionary.

Median as a weighted arithmetic mean of all Sample Observations
Calculations and comparison between arithmetic and geometric mean of two values

Источник

Recent Examples on the Web

An average of four chargers will be installed per store, Reuters reports.

—Marco Marcelline, PCMAG, 10 Apr. 2023

Emergency Supplemental Nutrition Assistance Program benefits introduced during the pandemic expired at the end of February, leaving roughly 600,000 to 700,000 Marylanders who receive food assistance short an average of $82 per month.

—Dillon Mullan, Baltimore Sun, 10 Apr. 2023

The Hawks score an average of 118.4 points per game, 8.6 more points than the 109.8 the Heat allow to opponents.

—Jeremy Cluff, The Arizona Republic, 10 Apr. 2023

Each battery can hold more than 3 MWh of energy—or about enough juice to power an average of 3,600 homes for one hour.

—Rachel Cormack, Robb Report, 10 Apr. 2023

From 2009 to 2018, such labs reported an average of 98 incidents annually, ranging from minor problems with protective gear to exposures from accidental jabs with contaminated needles, according to CDC records.

—Joby Warrick, Washington Post, 10 Apr. 2023

Last week, the volcano registered an unprecedented average of 6,000 earthquakes per day, likely caused by magma moving through the main fault system, says Colombia’s Geological Service (CGS).

—Chris Morris, Fortune, 10 Apr. 2023

Esaad closed on eight units Oct. 27 and another eight on Nov. 11, paying nearly $7.7 million for the 16 units — or an average of nearly $480,000 each, a bankruptcy document show.

—Patrick Danner, San Antonio Express-News, 10 Apr. 2023

Separate research Nagata has worked on indicates gay youths use screens an average of nearly four hours a day more than straight kids.

—Dan Avery, NBC News, 9 Apr. 2023

The average litter size is four pups.

—Dawn Stover, oregonlive, 12 Apr. 2023

Alabama Arise says the average family spends $600 a year on the state sales tax on food.

—Mike Cason | Mcason@al.com, al, 12 Apr. 2023

For The Dad Who Loves Flip Flops Oofos OOriginal Sandal These cushiony shoes are more than your average flip-flops.

—Lizzy Briskin, womenshealthmag.com, 12 Apr. 2023

For Sacramento, that’s essentially a roster-wide request; the average age of the Kings’ roster is 25.7.

—C.j. Holmes, San Francisco Chronicle, 11 Apr. 2023

Homes that have attributes such as a steam oven, quartz finishes or even hurricane shutters/windows, typically sell for a higher price than the average home, according to data from Zillow.

—Amber Bonefont, Sun Sentinel, 11 Apr. 2023

With more than 27 inches of precipitation on average, California’s recent wet season ranked as the eighth wettest.

—Terry Castleman, Los Angeles Times, 11 Apr. 2023

On average, lava can range between 1,300 to 2,200 degrees Fahrenheit, depending on its location.

—Olivia Munson, USA TODAY, 11 Apr. 2023

On average since drought began in 2000, the river has flowed about 12 million acre-feet a year, and the Bureau of Reclamation has users need to slash use by between 2 million and 4 million acre-feet.

—Brandon Loomis, The Arizona Republic, 11 Apr. 2023

Senior Veronica Puckett is batting .609 (14-for-23) with 15 runs scored and sophomore Jaylene Mieres averages .667 (12-for-18) with 13 RBI for the Wolves.

—J.c. Carnahan, Orlando Sentinel, 29 Mar. 2023

The work hour regulations went into effect July 2011, noting residents could only work a maximum of 80 hours per week averaged over a four-week period, per ACGME.

—Shiv Sudhakar, Fox News, 29 Mar. 2023

The high-scoring Red Stockings averaged 42 runs a game.

—Jeff Suess, The Enquirer, 29 Mar. 2023

The series became a global sensation, averaging 24 million viewers in the U.S., spawning several international spin-offs (and arguably the whole Real Housewives franchise), and returning the likes of Teri Hatcher and Felicity Huffman to the limelight.

—Erik Maza, Town & Country, 29 Mar. 2023

On the year, Cryer averaged 15 points per game and two assists while shooting 41.5% from deep.

—Michael Haag, Dallas News, 29 Mar. 2023

The 34-year-old has averaged 26.7 points and 7.3 rebounds (69.0% shooting) in three games with the Suns.

—Jeremy Cluff, The Arizona Republic, 29 Mar. 2023

Last year, regular-season games averaged 3:03.

—Jaylon Thompson, USA TODAY, 29 Mar. 2023

In 29 games this season, Winslow has averaged 6.8 points, 5.0 rebounds and 3.4 assists.

—Afentres, oregonlive, 29 Mar. 2023

See More

These examples are programmatically compiled from various online sources to illustrate current usage of the word ‘average.’ Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Источник

Average and mean are similar yet are different. The term average is the sum of all the numbers divided by the total number of values in the set. The term mean is finding of the average of a sample data. Average is finding the central value in math, whereas mean is finding the central value in statistics. We use average when the difference between the values is less, whereas, for the set of values that have more difference, we prefer finding the mean of the data.

Definition of Average

By definition, an average is the arithmetic mean of the sum of all the values divided by the total number of values in a given set. An average is calculated for those sets of value which are more or less same. The term average describes the numeric value that represents a large amount of data. An average can be derived by calculating the ratio of the sum of all the values to the number of units or values.

Let us look at an example to understand average better:

Example 1: Find the average of the set of numbers 3, 6, 14, 18, 20, 35, 44

Solution: The formula for finding the average is Sum of the Numbers/Number of Units

Sum of the numbers = 3 + 6 +14 + 18 + 20 + 35 + 44 = 140

Number of units = 7

Therefore, Average = Sum of Numbers/Number of Units

= 140/7

= 20

Hence, the average of the set of numbers is 20.

Definition of Mean

A mean is a mathematical term, that describes the average of a sample. In Statistics, the definition of the mean is similar to the average where it is the sum of all the given data values divided by the total number of data values given in the set. A mean is calculated for those sets of values with either more difference or those values that are close to each other. Mean has other forms as well such as the harmonic mean and geometric mean that are used in different situations.

Difference between Average and Mean

Mathematically, average and mean are similar to each other as it is used to explain the set of numbers. Listed below are the key points of average and mean that explain the difference in a table format.

Average	Mean
An Average can be defined as the sum of all numbers divided by the total number of values.	A mean can be defined as an average of the set of values in a sample of data.
In other words, an average is also called the arithmetic mean.	Describing the average is called a mean. There 2 other kinds of mean — harmonic and geometric mean.
An average is calculated for a set of numbers that are of the same value range.	Mean is mostly used in Statistics where the set of values have a vast difference or they are closely related to each other.
An average represents a single number from the list of numbers.	Mean is the central point among the set of numbers.
The usage of average is seen in day-to-day life as a conversation in the English language.	The usage of the mean is seen mostly in a technical and mathematical sense.
Through the average, we can also find out the values of the median and mode.	On the other hand, the mean does not give the median and mode even though all three — mean, median, and mode, work closely in Statistics.

Important Points

The average of any number series or group is always between its smallest and the largest value.
Average is used in day-to-day calculations whereas mean is the average that is mostly used in statistics while solving math questions.

Examples on Difference between Average and Mean

Example 1: A student has gotten the following grades on his tests: 82, 93, 79, and 69. He wants a 75 or better overall. What is the minimum grade he must get on the last test in order to achieve that average?

Solution:

We need to find out the minimum grade by adding all the grades given and divide it by the number of grades. Since we don’t have a score for the last test, let’s use the variable ‘x’ to determine the average.

(82 + 93 + 79 + 69 + x)/5 = 75

We move the five to the other side and multiply 5 with 75.

82 + 93 + 79 + 69 + x = 375

323 + x = 375

x = 375 — 323

x = 52

Hence, the student needs to score at least a 52 on the last test.
Example 2: Find the mean for the following data: 45, 76, 2, 10, 33.

Solution:

The given list is 45, 76, 2, 10, 33

Mean = Sum of observations/Total number of observations

= (45 + 76 + 2 + 10 + 33)/ 5

= 166/5

= 33.2

Therefore, the mean for the following list is 33.2

Show Solution >

go to slidego to slide

Great learning in high school using simple cues

Indulging in rote learning, you are likely to forget concepts. With Cuemath, you will learn visually and be surprised by the outcomes.

Book a Free Trial Class

Practice Questions on Difference between Average and Mean

View Answer >

go to slidego to slide

FAQs on Difference between Average and Mean

What is the Difference Between Mean and Average?

Average, also called the arithmetic mean, is the sum of all the values divided by the number of values. Whereas, mean is the average in the given data. In statistics, the mean is equal to the total number of observations divided by the number of observations.

How do you Calculate Mean vs Average?

The mean is the average of the numbers and to calculate both averages and mean we need to add up all the values, then divide by the total number of values. In other words, it is the sum of the values divided by the count of the values. The formulas for both are more or less the same. Average = Mean = Sum/Count

Does Average Always Reciprocates as Mean?

Since both average and mean are similar, yes average usually does reciprocate as mean. Average is also called that arithmetic mean and mean is the average of the sample data.

What is the Formula for the Average?

Average = Sum of the Observations/Number of Observations. For example, the average of 2,5,7,9, and 7 is 30 divided by 5 which is 6.

Why is Average Called Mean?

A mean can be defined as an average of the set of values in a sample of data. An average is referred to as the sum of all values divided by the total number of values. In mathematics, both the words mean and average are related but have their own difference as mentioned in this article.

Are Mean and Average Interchangeable?

Yes, most often average and mean are used interchangeably. In Statistics, instead of using the word average, the word mean is used. It does tend to create confusion as the basic meaning of both the words average and mean are the same.

Источник

Top Definitions
Quiz
Related Content
Average Vs. Mean Vs. Median Vs. Mode
Examples
British
Scientific
Cultural

This shows grade level based on the word’s complexity.

[ av-er-ij, av-rij ]

/ ˈæv ər ɪdʒ, ˈæv rɪdʒ /

This shows grade level based on the word’s complexity.

noun

a quantity, rating, or the like that represents or approximates an arithmetic mean: Her golf average is in the 90s. My average in science has gone from B to C this semester.

a typical amount, rate, degree, etc.; norm.

Mathematics. a quantity intermediate to a set of quantities.

Commerce.

a charge paid by the master of a ship for such services as pilotage or towage.
an expense, partial loss, or damage to a ship or cargo.
the incidence of such an expense or loss to the owners or their insurers.
an equitable apportionment among all the interested parties of such an expense or loss.Compare general average, particular average.

adjective

of or relating to an average; estimated by average; forming an average: The average rainfall there is 180 inches.

typical; common; ordinary: The average secretary couldn’t handle such a workload. His grades were nothing special, only average.

verb (used with object), av·er·aged, av·er·ag·ing.

to find an average value for (a variable quantity); reduce to a mean: We averaged the price of milk in five neighborhood stores.

(of a variable quantity) to have as its arithmetic mean: Wheat averages 56 pounds to a bushel.

to do or have on the average: He averages seven hours of sleep a night.

verb (used without object), av·er·aged, av·er·ag·ing.

to have or show an average: to average as expected.

Verb Phrases

average down, to purchase more of a security or commodity at a lower price to reduce the average cost of one’s holdings.

average out,

to come out of a security or commodity transaction with a profit or without a loss.
to reach an average or other figure: His taxes should average out to about a fifth of his income.

average up, to purchase more of a security or commodity at a higher price to take advantage of a contemplated further rise in prices.

QUIZ

CAN YOU ANSWER THESE COMMON GRAMMAR DEBATES?

There are grammar debates that never die; and the ones highlighted in the questions in this quiz are sure to rile everyone up once again. Do you know how to answer the questions that cause some of the greatest grammar debates?

Which sentence is correct?

Idioms about average

on the / an average, usually; typically: She can read 50 pages an hour, on the average.

Origin of average

1485–95; earlier averay charge on goods shipped, originally duty (<Middle French avarie<Old Italian avaria<Arabic ʿawārīyah damaged merchandise), with -age replacing -ay

OTHER WORDS FROM average

av·er·age·a·ble, adjectiveav·er·age·ly, adverbav·er·age·ness, nounsub·av·er·age, adjective

sub·av·er·age·ly, adverbsu·per·av·er·age, adjectivesu·per·av·er·age·ness, nounun·av·er·aged, adjectiveun·der·av·er·age, adjectivewell-av·er·aged, adjective

Words nearby average

Aventine, aventurine, avenue, Avenzoar, aver, average, average adjuster, average deviation, average joe, average life, average revenue

Dictionary.com Unabridged
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2023

AVERAGE VS. MEAN VS. MEDIAN VS. MODE

What’s the difference between average, mean, median, and mode?

In the context of mathematics and statistics, the word average refers to what’s more formally called the mean, which is the sum of a set of values divided by the number of values. In contrast, the median is the middle number in a set of values when those values are arranged from smallest to largest, while the mode of a set of values is the most frequently repeated value in the set.

The word average is of course also very commonly used in more general ways. In math, though, it’s helpful to use more specific terms when determining the most representative or common value in a set of numbers.

To illustrate the difference, let’s look at an example set of seven values: 2, 3, 3, 4, 6, 8, 9.

To get the mean of this set, you’d add up all the values (2+3+3+4+6+8+9=35) and then divide that total by the number of values (7), resulting in a mean of 5. This is what most people are referring to when they refer to the average of some set of numbers.

To find the median, you have to find the one that’s sequentially in the middle. In a set of seven numbers arranged in increasing value, the median is the fourth number (since there are three before and three after). In this set (2, 3, 3, 4, 6, 8, 9), the median is 4. When a set has an even number of values, the median is the mean of the two middle values.

The mode is simply the value that shows up the most. In the example set, the mode is 3, since it occurs twice and all the other values occur only once.

Want to learn more? Read the full breakdown of the difference between average, mean, median, and mode.

Quiz yourself on average vs. mean vs. median vs. mode!

Should average, mean, median, or mode be used in the following sentence?

The most frequently repeated test score is 80, so it’s the _____ of the set.

Words related to average

mediocre, moderate, ordinary, regular, median, standard, boilerplate, common, commonplace, fair, familiar, garden, general, humdrum, intermediate, mainstream, medium, middling, nowhere, plastic

How to use average in a sentence

That is roughly in line with a Post average of recent polls from the state that put Biden’s advantage at seven points.
FiveThirtyEight’s average of state polls at the end of the 2016 race gave Clinton a five-point lead in Wisconsin and an eight-point lead in Minnesota.
Since the lockout of 2004-05, five cup winners have averaged fewer goals per game.
The Wisconsin poll is consistent with other recent polls in the state, with The Post’s average showing Biden’s margin at seven points, narrower than in midsummer but not much different from what it was immediately after the GOP convention.

That is a somewhat larger margin than a Washington Post average of recent polls in the state, which shows Biden’s lead to be seven percentage points.
Well over a thousand holes in, I average less than four strokes per hole.
On average, the vaccine has an efficacy of about 60 percent.
Average age ranges from 45 to 65, with her youngest client at 18 and the oldest in her 80s.
Ramos was 38—nearly two decades older than the average recruit.
All because Murthy believes that gun violence, which kills an average of 86 Americans every day, is a public health issue.
I do not think the average number of passengers on a corresponding route in our country could be so few as twenty.
Though the average speaker is generally limited by one type of voice, which he varies somewhat, it is not often disguised.
I should judge that a peck of corn is about the average product of a day’s work through all this region.
The average citizen of three generations ago was probably not aware that he was an extreme individualist.
He was a pretty bright sort, that same Goodell, quick-witted, nimble of tongue above the average Englishman.

British Dictionary definitions for average

noun

the typical or normal amount, quality, degree, etcabove average in intelligence

Also called: arithmetic mean the result obtained by adding the numbers or quantities in a set and dividing the total by the number of members in the setthe average of 3, 4, and 8 is 5

(of a continuously variable ratio, such as speed) the quotient of the differences between the initial and final values of the two quantities that make up the ratiohis average over the journey was 30 miles per hour

maritime law

a loss incurred or damage suffered by a ship or its cargo at sea
the equitable apportionment of such loss among the interested parties

(often plural) stock exchange a simple or weighted average of the prices of a selected group of securities computed in order to facilitate market comparisons

on average, on the average or on an average usually; typicallyon average, he goes twice a week

adjective

usual or typical

mediocre or inferiorhis performance was only average

constituting a numerical averagethe average age; an average speed

approximately typical of a range of valuesthe average contents of a matchbox

verb

(tr) to obtain or estimate a numerical average of

(tr) to assess the general quality of

(tr) to perform or receive a typical number ofto average eight hours’ work a day

(tr) to divide up proportionatelythey averaged the profits among the staff

(tr) to amount to or be on averagethe children averaged 15 years of age

(intr) stock exchange to purchase additional securities in a holding whose price has fallen (average down) or risen (average up) in anticipation of a speculative profit after further increases in price

Derived forms of average

averagely, adverbaverageness, noun

Word Origin for average

C15 averay loss arising from damage to ships or cargoes (shared equitably among all concerned, hence the modern sense), from Old Italian avaria, ultimately from Arabic awār damage, blemish

Collins English Dictionary — Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

Scientific definitions for average

A number, especially the arithmetic mean, that is derived from and considered typical or representative of a set of numbers. Compare arithmetic mean median mode.

The American Heritage® Science Dictionary
Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

Cultural definitions for average

A single number that represents a set of numbers. Means, medians, and modes are kinds of averages; usually, however, the term average refers to a mean.

The New Dictionary of Cultural Literacy, Third Edition
Copyright © 2005 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

Источник

Other forms: averaged; averaging; averages; averagely

If something is average, it’s ordinary and not very special. You might say a movie was average if you thought it was just okay.

Average can describe what’s true most of the time, as in, “The average rainfall in Seattle is fifty-two inches.” It can also be used in a mathematical and more precise way. On his English tests, Dylan received grades of 92%, 85% and 94%. His average grade was 90%, or the sum of the test scores divided by the number of tests taken.

Definitions of average

noun

an intermediate scale value regarded as normal or usual

“he is about
average in height”

“the snowfall this month is below
average”
noun

a statistic describing the location of a distribution
noun

(sports) the ratio of successful performances to opportunities

see moresee less

types:

batting average, hitting average

(baseball) a measure of a batter’s performance; the number of base hits divided by the number of official times at bat

fielding average

(baseball) a measure of a fielder’s performance; the number of assists and putouts divided by the number of chances

type of:

ratio

the relative magnitudes of two quantities (usually expressed as a quotient)
adjective

around the middle of a scale of evaluation

“an orange of
average size”

synonyms:

intermediate, medium

moderate

being within reasonable or average limits; not excessive or extreme
adjective

approximating the statistical norm or average or expected value

“the
average income in New England is below that of the nation”

“of
average height for his age”

synonyms:

mean

normal

conforming with or constituting a norm or standard or level or type or social norm; not abnormal
adjective

relating to or constituting the most frequent value in a distribution

synonyms:

modal

normal

conforming with or constituting a norm or standard or level or type or social norm; not abnormal
adjective

relating to or constituting the middle value of an ordered set of values (or the average of the middle two in a set with an even number of values)

synonyms:

median

normal

conforming with or constituting a norm or standard or level or type or social norm; not abnormal
verb

amount to or come to an average, without loss or gain
verb

achieve or reach on average
verb

compute the average of
adjective

lacking special distinction, rank, or status; commonly encountered

“average people”

synonyms:

ordinary

common

having no special distinction or quality; widely known or commonly encountered; average or ordinary or usual
adjective

lacking exceptional quality or ability

“a novel of
average merit”

“the caliber of the students has gone from mediocre to above
average”

synonyms:

fair, mediocre, middling

ordinary

not exceptional in any way especially in quality or ability or size or degree

DISCLAIMER: These example sentences appear in various news sources and books to reflect the usage of the word ‘average’.
Views expressed in the examples do not represent the opinion of Vocabulary.com or its editors.
Send us feedback

Commonly confused words

mean / median / average

Wordsmiths sometimes dislike numbers, or at least have a hard time grasping them. These words offer us an opportunity to better understand numbers and use their terms more precisely in writing and speaking.

EDITOR’S CHOICE

Look up average for the last time

Close your vocabulary gaps with personalized learning that focuses on teaching the
words you need to know.

Sign up now (it’s free!)

Whether you’re a teacher or a learner, Vocabulary.com can put you or your class on the path to systematic vocabulary improvement.

Get started

Источник

At Tavoy, on the Tenasserim coast, the maximum rate of productiveness of the rice land was, in 1825, and is still believed to be, nearly the same as the average of Siam; while their _average_ was only twenty-fold. ❋ P. L. Simmonds (N/A)

The average weight of brain, in 278 Europeans, was 49.50 oz., in 24 White American soldiers, 52.06 oz., indicating a greater _average_ for the American brain. ❋ Ray Vaughn Pierce (1877)

_average_ novel of the third quarter of the century — in a more than average but not of an extraordinary, transcendental, or quintessential condition — Anthony Trollope is about as good a representative as can be found. ❋ George Saintsbury (1889)

f, densitometry of the bands from (e), normalized to β-actin; N = normal brain, S = sham, C = contra-lateral, I = ischemic; Graph depicts the average of at least three separate experiments, and the average+ / − the S.E.M. is shown; Panel III. ❋ Unknown (2009)

Means, medians, and modes are kinds of averages; usually, however, the term average refers to a mean. ❋ Unknown (2002)

The term average originally meant what is now distinguished as general average; and the expression ❋ Various (N/A)

What «Average» means — Many of us use the term average when we discuss metrics, this is a great primer to understand the term better. ❋ Unknown (2008)

The numbers are even higher in places like Chicago, where the average is almost $42,000. ❋ Akito Yoshikane (2010)

The long-term average is about 80%, and with current growth rates we should be there in a year. ❋ Brian S. Wesbury (2010)

Once decided that idea needs to be written, not once but rewritten several times (my average is around six drafts per story) ❋ Unknown (2010)

Sure, there’s a litany of movies based on King’s stories, and the average is about half-good and half-bad. ❋ Unknown (2009)

For some, the average turns out to be a recognizable image; for others the average is a colored blob. ❋ Unknown (2008)

Even for Pope and Young bucks, the average is around 21 yards. ❋ Unknown (2008)

Anyway the average is about two or three day and the risk could be called 15 per million per year. ❋ Newmania (2007)

[So what] do you think of her?
well, She’s average.
So Would you do her?
Well, if I was drunk and [I never] [had to] talk to her again. ❋ JP$ (2003)

Sally: Did you [shack up] last night?
[Joanna]: Yes, at [Charlie’s].
Sally: Well…how was it??!!
Joanna: Eh, average. ❋ Annie May (2005)

Levi: WTF? There’s no pics on this chick’s profile.
Nate: What’s her weight entry say?
Levi: Average. Profile says she’s «curvy».
Nate: Means she’s average in American terms, not French. Her curves are rolls.
Feminist from the [woodwork]: It’s what’s inside that counts!
[Fat Goth] Girl: Fat girls need love too!
Nate: *shotgun fires four times, once each and then once each to make sure* Not from me; and a tranny once told me the same thing about the inside.
Levi: You only get what you give. Get back in your [badgerhole], ya bitch. ❋ Derek Peavey (2006)

[SWF], [30] average in [size] looking for an eating partner. ❋ Xzybit (2005)

The [average american] household has [2.4] cars and [2.5] children. ❋ «better Geeky Than Stupid» (2009)

Wife- «[Hi honey], how was [work]?»
Husband- «[Oh], it was average.» ❋ The Governor (2004)

[Rick] is average ❋ G (2003)

1. Man, my new [computer] is average.
2. That was a pretty average [performance] by my [local] sports team.
3. You are an average. ❋ Chewy (2005)

«Ugh! Let’s leave. This [bar] couldn’t have more averagers.»
«Don’t [join] that [frat]! Look who’s in it! It’s just one averager after another.» ❋ Wren1776 (2008)

most of [america], Average ❋ Thewoman (2010)

Источник

average — n Average, mean, median, norm, par denote something and usually a number, a quantity, or a condition that represents a middle point between extremes. Of these words average, mean, median, and par are also used as adjectives. Average is an… … New Dictionary of Synonyms

average — [av′ər ij, av′rij] n. [altered (by assoc. with ME average, money rent paid in place of service by the tenant with his horses < aver, draft horse) < OFr avarie, damage to ship or goods, mooring charges < OIt avaria < Ar ʿ awār, damaged … English World dictionary

average — I (midmost) adjective center, centermost, intermediate, mean, mean proportioned, medial, median, mediate, medium, mid, middle, middle class, middle grade, middlemost, middling associated concepts: average annual earnings or wages, average capital … Law dictionary

Average — Av er*age, n. [OF. average, LL. averagium, prob. fr. OF. aver, F. avoir, property, horses, cattle, etc.; prop. infin., to have, from L. habere to have. Cf. F. av[ e]rage small cattle, and avarie (perh. of different origin) damage to ship or cargo … The Collaborative International Dictionary of English

Average — Av er*age, a. 1. Pertaining to an average or mean; medial; containing a mean proportion; of a mean size, quality, ability, etc.; ordinary; usual; as, an average rate of profit; an average amount of rain; the average Englishman; beings of the… … The Collaborative International Dictionary of English

Average — Av er*age, v. i. To form, or exist in, a mean or medial sum or quantity; to amount to, or to be, on an average; as, the losses of the owners will average twenty five dollars each; these spars average ten feet in length. [1913 Webster] … The Collaborative International Dictionary of English

average — [adj1] normal, typical boilerplate*, common, commonplace, customary, dime a dozen*, everyday, fair, fair to middling*, familiar, garden*, garden variety*, general, humdrum*, intermediate, mainstream, mediocre, medium, middle of the road*,… … New thesaurus

average — ► NOUN 1) the result obtained by adding several amounts together and then dividing the total by the number of amounts. 2) a usual amount or level. ► ADJECTIVE 1) constituting an average. 2) usual or ordinary. 3) mediocre. ► … English terms dictionary

Average — Av er*age, v. t. [imp. & p. p. {Averaged} (?); p. pr. & vb. n. {Averaging}.] 1. To find the mean of, when sums or quantities are unequal; to reduce to a mean. [1913 Webster] 2. To divide among a number, according to a given proportion; as, to… … The Collaborative International Dictionary of English

avérage — 1. (a vé ra j ) s. m. Terme de commerce. La moyenne avérée, vraie, reconnue telle, et en général la moyenne. Sur trois ans l avérage a été de…. ÉTYMOLOGIE Avérer. avérage 2. (entrée créée par le supplément) (a vé ra j ) s. m. Nom, dans le… … Dictionnaire de la Langue Française d’Émile Littré

average — (del inglés; pronunciamos averás ) sustantivo masculino 1. Área: deporte Promedio, término medio: Gana el Barcelona por gol average … Diccionario Salamanca de la Lengua Española

Источник

English[edit]

Etymology 1[edit]

From Middle French avarie, from Old French avarie, from Old Italian avaria (which is possibly from Arabic عَوَارِيَّة‎ (ʕawāriyya, “damaged goods”), from عَوَار‎ (ʕawār, “fault, blemish, defect, flaw”), from عَوِرَ‎ (ʕawira, “to lose an eye”)) + English suffix -age.

Pronunciation[edit]

(Received Pronunciation, US) enPR: ăvʹərĭj, ăvʹrĭj IPA^(key): /ˈævəɹɪd͡ʒ/, /ˈævɹɪd͡ʒ/

Noun[edit]

average (plural averages)

(mathematics) The arithmetic mean.
- 2013 June 1, “Towards the end of poverty”, in The Economist‎^[1], volume 407, number 8838, page 11:
  
  But poverty’s scourge is fiercest below $1.25 (the average of the 15 poorest countries’ own poverty lines, measured in 2005 dollars and adjusted for differences in purchasing power): people below that level live lives that are poor, nasty, brutish and short.
The average of 10, 20 and 24 is (10 + 20 + 24)/3 = 18.
(statistics) Any measure of central tendency, especially any mean, the median, or the mode. [from c. 1735]
(law, marine) Financial loss due to damage to transported goods; compensation for damage or loss. [from 15th c.]
- 2008, Filiberto Agusti, Beverley Earle, Richard Schaffer, Filiberto Agusti, Beverley Earle, International Business Law and Its Environment, page 219,
  
  Historically, the courts have allowed a general average claim only where the loss occurred as a result of the ship being in immediate peril. […] The court awarded the carrier the general average claim. It noted that “a ship′s master should not be discouraged from taking timely action to avert a disaster,” and need not be in actual peril to claim general average.
Customs duty or similar charge payable on transported goods.
Proportional or equitable distribution of financial expense.
(sports) An indication of a player’s ability calculated from his scoring record, etc.

batting average

Usage notes[edit]

(mathematics, statistics): The term average may refer to the statistical mean, median or mode of a batch, sample, or distribution, or sometimes any other measure of central tendency. Statisticians and responsible news sources are careful to use whichever of these specific terms is appropriate. In common usage, average refers to the arithmetic mean. It is, however, a common rhetorical trick to call the most favorable of mean, median and mode the «average» depending on the interpretation of a set of figures that the speaker or writer wants to promote.

Coordinate terms[edit]

(measure of central tendency): arithmetic mean, geometric mean, harmonic mean, mean, median, mode

Derived terms[edit]

above average
arithmetic average
average atomic mass
averager
batting average
below average
bowling average
earned run average
general average
goal average
grade point average
height above average terrain
law of averages
moving average
national average
on average
particular average
rolling average
slugging average
subaverage
time average
weighted average
weighted-average cost of capital
z-average

Translations[edit]

arithmetic mean

Armenian: միջին (hy) (miǰin)
Bhojpuri: औसत (ausat)
Bulgarian: средно число (sredno čislo)
Catalan: mitjana (ca) f
Chinese:

Cantonese: 平均 (ping⁴ gwan¹)

Mandarin: 平均 (zh) (píngjūn)
Czech: průměr (cs) m
Danish: gennemsnit (da) n, middelværdi (da) c
Dutch: gemiddelde (nl) n
Esperanto: meznombro, aritmetika meznombro
Faroese: miðaltal n
Finnish: keskiarvo (fi)
French: moyenne (fr) f
Georgian: საშუალო (sašualo)
German: Durchschnitt (de) m, arithmetisches Mittel n, Mittelwert (de) m
Greek: μέσος όρος m (mésos óros)

Ancient: μεσότης f (mesótēs)
Greenlandic: agguaqatigiissitaq
Hebrew: ממוצע‎ (he) m (memutza)
Hungarian: átlag (hu)
Icelandic: meðaltal n
Italian: media (it) f
Japanese: 平均 (ja) (へいきん, heikin)
Korean: 평균 (ko) (pyeonggyun)
Malay: purata (ms), pukul rata (ms), hitung panjang, rerata, rata-rata
Malayalam: ശരാശരി (ml) (śarāśari)
Maori: toharite, tau toharite
Norwegian:

Bokmål: gjennomsnitt n, middeltall

Nynorsk: gjennomsnitt n, medeltal
Plautdietsch: Derchschnett m
Polish: średnia (pl)
Portuguese: média (pt) f
Romanian: medie (ro) f
Russian: сре́днее (ru) n (srédneje)
Scottish Gaelic: meadhan m, cuibheasachd f, cuibheas m
Serbo-Croatian: prosjek (sh) m, prosek (sh) m

Cyrillic: про̏сјечан / про̏сечан

Roman: prȍsječan (sh) / prȍsečan
Slovak: priemer m
Spanish: promedio (es) m, media (es)
Swedish: genomsnitt (sv) n, medeltal (sv) n
Telugu: సగటు (te) (sagaṭu), సరాసరి (te) (sarāsari)
Ukrainian: сере́днє (serédnje)

any measure of central tendency

Arabic: مُعَدَّل‎ m (muʕaddal)

Egyptian Arabic: مُتَوَسِّط‎ m (mutawasseṭ), معدل‎ m (mu’adal)
Bulgarian: средно (bg) n (sredno)
Finnish: keskiarvo (fi)
Japanese: 平均 (ja) (へいきん, heikin)
Kurdish:

Central Kurdish: ڕادەی ئاسایی‎ (radey asayî)
Plautdietsch: Derchschnett m
Scottish Gaelic: meadhan m
Telugu: సగటు (te) (sagaṭu), సరాసరి (te) (sarāsari)

Adjective[edit]

average (comparative more average, superlative most average)

(not comparable) Constituting or relating to the average.

The average age of the participants was 18.5.
Neither very good nor very bad; rated somewhere in the middle of all others in the same category.

I soon found I was only an average chess player.
Typical.
- 2002, Andy Turnbull, The Synthetic Beast: When Corporations Come to Life, page 12,
  
  We tend to think that exceptionally attractive men and women are outstanding but the fact is that they are more average than most.
- 2004, Deirdre V. Lovecky, Different Minds: Gifted Children with AD/HD, Asperger Syndrome, and Other Learning Deficits, page 75,
  
  Things that never would occur to more average children, with and without AD/HD, will give these children nightmares.
- 2009, Susan T. Fiske, Social Beings: Core Motives in Social Psychology, page 73,
  
  In other words, highly attractive people like highly attractive communicators and more average people like more average communicators.
The average family will not need the more expensive features of this product.
(informal) Not outstanding, not good, banal; bad or poor.
- 2002, Andy Slaven, Video Game Bible, 1985-2002, page 228,
  
  The graphics, sound, and most everything else are all very average. However, the main thing that brings this game down are the controls — they feel very clumsy and awkward at times.
- 2005, Brad Knight, Laci Peterson: The Whole Story: Laci, Scott, and Amber’s Deadly Love Triangle, page 308,
  
  But what the vast majority of the populace doesn′t realise is the fact that he′s only on TV because he became famous from one case, Winona Ryder’s, which, by the way, he lost because he′s only a very average attorney.
- 2009, Carn Tiernan, On the Back of the Other Side, page 62,
  
  In the piano stool there was a stack of music, mostly sentimental ballads intended to be sung by people with very average voices accompanied by not very competent pianists.

Synonyms[edit]

(constituting or relating to the average): av., ave., avg., expectation (colloquial), mean
(neither very good nor very bad): mediocre, medium, middle-ranking, middling, unremarkable, so-so, comme ci comme ça
(typical): conventional, normal, regular, standard, typical, usual, bog-standard (slang)
(not outstanding, not good; bad or poor): ordinary, uninspiring

Antonyms[edit]

(neither very good nor very bad): extraordinary

Derived terms[edit]

average bear
average frustrated chump
average Joe
averagely
averageness
daily average revenue trades

Translations[edit]

constituting or relating to the average

Arabic: مُتَوَسِّط‎ (mutawassiṭ), مُعَدَّل‎ (muʕaddal)
Armenian: միջին (hy) (miǰin)
Belarusian: сярэ́дні (be) (sjarédni)
Bulgarian: среден (bg) (sreden)
Chinese:

Mandarin: 平均 (zh) (píngjūn)
Czech: průměrný (cs) m
Danish: gennemsnitlig
Dutch: gemiddelde (nl)
Esperanto: mezgranda
Finnish: keskimääräinen (fi)
French: moyen (fr) m
Galician: media f
German: durchschnittlich (de)
Greek:

Ancient: μέτριος (métrios)
Hungarian: átlagos (hu)
Irish: meánach, meán-, coitianta, gnách
Italian: medio (it) m, media (it) f
Japanese: 平均 (ja) (へいきん, heikin)
Korean: 평균의 (ko) (pyeonggyunui)
Latin: mediocris (la)
Macedonian: просечен (prosečen)
Norwegian:

Bokmål: gjennomsnittlig, middels

Nynorsk: gjennomsnittleg, middels
Old English: medume
Persian: متوسط‎ (fa) (motavasset, motevasset)
Polish: średni (pl) m
Portuguese: médio (pt) f, média (pt) f
Romanian: mediu (ro), mijlociu (ro)
Russian: сре́дний (ru) (srédnij)
Scottish Gaelic: meadhanach, cuibheasach
Serbo-Croatian:

Cyrillic: про̏сјечан / про̏сечан

Roman: prȍsječan (sh) / prȍsečan
Slovak: priemerný
Slovene: povprečen (sl)
Spanish: medio (es)
Swedish: genomsnittlig (sv)
Tagalog: balasak
Telugu: సగటు (te) (sagaṭu)
Thai: โดยเฉลี่ย (dooi-chà-lìia)
Ukrainian: сере́дній (serédnij)
Vietnamese: trung bình (vi)
Welsh: canolog (cy)

neither very good nor very bad

Armenian: միջին (hy) (miǰin)
Bulgarian: среден (bg) (sreden)
Chinese:

Mandarin: 一般 (zh) (yībān)
Czech: průměrný (cs) m
Finnish: keskinkertainen (fi), keskimääräinen (fi)
Greek:

Ancient: μέτριος (métrios)
Hungarian: átlagos (hu)
Japanese: 平凡な (ja) (へいぼんな, heibon-na)
Latin: mediocris (la)
Norman: pâssabl’ye m or f
Old English: medeme
Polish: przeciętny (pl) m
Portuguese: equilibrado (pt) m
Russian: сре́дний (ru) (srédnij), обы́чный (ru) (obýčnyj)
Scottish Gaelic: meadhanach, cuibheasach
Serbo-Croatian:

Cyrillic: про̏сјечан / про̏сечан

Roman: prȍsječan (sh) / prȍsečan
Slovak: priemerný
Slovene: navaden
Spanish: ni fu ni fa (es), promedio (es), mediocre (es)
Telugu: మోస్తరు (te) (mōstaru)

typical

Armenian: միջին (hy) (miǰin)
Bulgarian: нормален (bg) (normalen), обикновен (bg) (obiknoven)
Chinese:

Mandarin: 普通 (zh) (pǔtōng)
Czech: průměrný (cs) m
Finnish: tavallinen (fi), tyypillinen (fi)
French: moyen (fr)
Hungarian: (as a prefix in compounds) átlag- (hu)
Japanese: 平凡な (ja) (へいぼんな, heibon-na), 普通の (ja) (ふつうの, futsū-no)
Old English: medeme
Polish: przeciętny (pl) m
Russian: обыкнове́нный (ru) (obyknovénnyj), обы́чный (ru) (obýčnyj), среднестатисти́ческий (ru) (srednestatistíčeskij)
Serbo-Croatian:

Cyrillic: про̏сјечан / про̏сечан

Roman: prȍsječan (sh) / prȍsečan
Spanish: común y corriente
Swedish: typisk (sv)
Telugu: సగటు (te) (sagaṭu)
Ukrainian: пересічний (peresičnyj), середньостатисти́чний (serednʹostatystýčnyj)

Verb[edit]

average (third-person singular simple present averages, present participle averaging, simple past and past participle averaged)

(transitive) To compute the average of, especially the arithmetic mean.

If you average 10, 20 and 24, you get 18.
(transitive) Over a period of time or across members of a population, to have or generate a mean value of.

The daily high temperature last month averaged 15°C.

I averaged 75% in my examinations this year.
- 1961 November, “Talking of Trains: The roller-bearing A1s”, in Trains Illustrated, page 643:
  
  The five roller-bearing A1s are now averaging 120,000 miles between shopping; this figure is an improvement of about 50 per cent on the norm of other ex-L.N.E. Pacific types.
(transitive) To divide among a number, according to a given proportion.

to average a loss
(intransitive) To be, generally or on average.
- 1872 Elliott Coues, Key to North American Birds
  
  Gulls average much larger than terns, with stouter build […]

Derived terms[edit]

average down
average out
average up
averageable
unaveraged

Translations[edit]

to have or generate a mean value of

Bulgarian: усреднявам (usrednjavam)

Etymology 2[edit]

From Middle English average, from Medieval Latin averagium, from aver (“horse or other beast of burden, service required from the same”) from Old English eafor (“obligation to carry goods and convey messages for one’s lord”) from aferian (“to remove, take away”); + -age.

Noun[edit]

average (plural averages)

(UK, law, obsolete) The service that a tenant owed his lord, to be done by the animals of the tenant, such as the transportation of wheat, turf, etc.

German[edit]

Etymology[edit]

Borrowed from English average.

Pronunciation[edit]

IPA^(key): [ˈævəɹɪd͡ʒ], [ˈɛvəʁɪtʃ]
Hyphenation: ave‧rage

Adjective[edit]

average (indeclinable)

(dated, business) average

Middle French[edit]

Etymology[edit]

The Französisches Etymologisches Wörterbuch derives the word from Old French aver +‎ -age, where aver means «cattle» and is cognate to English aver (“work-horse, working ox, or other beast of burden”).^[1] The Shorter Oxford English Dictionary (1993) compares it to Medieval Latin averagium, from averia (“beast of burden”) (which the Französisches Etymologisches Wörterbuch in turn links to habeō (“to have”)).

Noun[edit]

average m (plural averages)

average (service that a tenant owed his lord, to be done by the animals of the tenant, such as the transportation of wheat, turf, etc.)

References[edit]

average on Dictionnaire du Moyen Français (1330–1500) (in French)
Godefroy, Frédéric, Dictionnaire de l’ancienne langue française et de tous ses dialectes du IX^e au XV^e siècle (1881) (average)

^ Walther von Wartburg (1928–2002), “habere”, in Französisches Etymologisches Wörterbuch (in German), volume 4: G H I, page 363

Источник

Question

Обновлено на

8 окт. 2019

Японский

Английский (американский вариант)
Итальянский
Японский

Вопрос про Английский (американский вариант)

When you «disagree» with an answer

The owner of it will not be notified.
Only the user who asked this question will see who disagreed with this answer.

Английский (американский вариант)
Филиппинский язык

In normal speech, mean and average both mean the same thing.

Английский (американский вариант)

In a math sense, they are identical.

However, average can also mean «normal» and mean can also mean «rude» or «the definition of something.»

Английский (американский вариант)

@ghetty2223 they are the same in math. But if not in math then ‘average’ is like “normal” and ‘mean’ is like “rude, aggressive”.
In math they both are adding and then dividing by how many numbers.
“12 is the mean (average) of 11,12,and 13” that is like 11+12+13=36, the 36/3=12.

Английский (американский вариант)

«Average» is the more common of the two in everyday conversation, and can be used very generally. Examples:

«It takes me an average of 30 minutes to get to work.»
«The average annual salary at this company is above $80,000.»
«I’m just an average guy after all.»

«Mean» is a slightly more specific and technical-sounding term, and it is used a lot when working with statistics. Unlike «average», you can’t use it to mean «ordinary» (like in the last example above). Examples:

«The mean of the distribution is 12.4 with a standard deviation of 1.6.»
«Her score was almost three standard deviations above the mean.»
«The theory was dismissed after it was discovered that the trends in the data could all be explained by regression towards the mean.»

If you study mathematics, you might know that there are various different kinds of «mean»: arithmetic mean, geometric mean, harmonic mean, etc. Normally the word «mean» refers to the arithmetic mean. The word «average» always refers to the arithmetic mean.

Английский (американский вариант)

They both mean the same thing.
The average of 10, 14 is 12
The mean of 10, 14 is 12

And here’s a math joke!
“My teacher called me average, how mean!”

Английский (американский вариант)

@IAmNotEmma you need tone careful: math jokes are the first sine of madness.

[News] Эй, привет! Тот, кто учит язык!

Вы знаете как улучшить свои языковые навыки❓ Все, что вам нужно – это исправление вашего письма носителем языка!
С HiNative ваше письмо носители языка могут исправить бесплатно ✍️✨.

Зарегистрироваться

В чем разница между average и mean ?

ответ

If you are talking statistics, average could be the median, mean, or mode. However, mean is commonly called «the average.»
В чем разница между universal и average ?

ответ

Universal comes from universe, it means something everyone does or has

Average is mathematical but it’s used to say “normal”
В чем разница между average и mean ?

ответ

Average can mean mean mode midrange or median.
В чем разница между mean и malice ?

ответ

I think mean is more of a descriptive word (like fun or boring) while malice is more like a quality (like energy, ease or hostility)

You cou…
В чем разница между average и mean ?

ответ

In terms of statistics, average and mean both mean the same thing.
В чем разница между universal и average ?

ответ

Although both universal and average are have no relation. Average and standard, above average, below average, have some relation.
В чем разница между average и mean ?

ответ

In math, they are the same thing
В чем разница между average и mean ?

ответ

In terms of math and statistics, mean and average are the same thing.

I’m below average. What does it mean?
The average number of family members in Japan is about three to four. это звучит нормально?
what is the average age do you think you started to read and write?

В чем разница между man и men ?
В чем разница между the 13rd of December и the 13th of December ?
В чем разница между I’m down for it и I’m up for it ?
В чем разница между signature и printed name ?
В чем разница между rape и molest ?

В чем разница между Саша, как говорить «собака» по-английски? и Саша, как сказать»собака» по-англ…
В чем разница между чайник долго закипает и чайник долго не закипает ?
В чем разница между будет запущена и запустится ?
В чем разница между Стучать у двери и стучать в дверь ?
В чем разница между ларёк и Забегаловка ?

В чем разница между добраться до дома и добраться домой; и добраться до Москвы и добраться в Моск…
В чем разница между Саша, как говорить «собака» по-английски? и Саша, как сказать»собака» по-англ…
В чем разница между чайник долго закипает и чайник долго не закипает ?
В чем разница между будет запущена и запустится ?
В чем разница между Стучать у двери и стучать в дверь ?

Previous question/ Next question

Как сказать на Корейский? school
Как сказать на Корейский? korean

Что означает этот символ?

Символ показывает уровень знания интересующего вас языка и вашу подготовку. Выбирая ваш уровень знания языка, вы говорите пользователям как им нужно писать, чтобы вы могли их понять.

Мне трудно понимать даже короткие ответы на данном языке.
Могу задавать простые вопросы и понимаю простые ответы.
Могу формулировать все виды общих вопросов. Понимаю ответы средней длины и сложности.
Понимаю ответы любой длины и сложности.

Подпишитесь на Премиум и сможете воспроизводить аудио/видеоответы других пользователей.

Что такое «подарки»?

Show your appreciation in a way that likes and stamps can’t.

By sending a gift to someone, they will be more likely to answer your questions again!

If you post a question after sending a gift to someone, your question will be displayed in a special section on that person’s feed.

Устали искать? HiNative может помочь вам найти ответ, который вы ищете.

Источник

General properties[edit]

Pythagorean means[edit]

Statistical location[edit]

Mode[edit]

Median[edit]

Mid-range[edit]

Summary of types[edit]

Miscellaneous types[edit]

Average percentage return and CAGR[edit]

Moving average[edit]

History[edit]

Origin[edit]

Etymology[edit]

Averages as a rhetorical tool[edit]

See also[edit]

References[edit]

External links[edit]

Definition of Average

Definition of Mean

Difference between Average and Mean

Related Topics

Important Points

Examples on Difference between Average and Mean

Practice Questions on Difference between Average and Mean

FAQs on Difference between Average and Mean

What is the Difference Between Mean and Average?

How do you Calculate Mean vs Average?

Does Average Always Reciprocates as Mean?

What is the Formula for the Average?

Why is Average Called Mean?

Are Mean and Average Interchangeable?

Idioms about average

Origin of average

OTHER WORDS FROM average

Words nearby average

AVERAGE VS. MEAN VS. MEDIAN VS. MODE

What’s the difference between average, mean, median, and mode?

Quiz yourself on average vs. mean vs. median vs. mode!

Words related to average

How to use average in a sentence

British Dictionary definitions for average

Derived forms of average

Word Origin for average

Scientific definitions for average

Cultural definitions for average

mean / median / average

Look up average for the last time

Sign up now (it’s free!)

Whether you’re a teacher or a learner, Vocabulary.com can put you or your class on the path to systematic vocabulary improvement.

English[edit]

Etymology 1[edit]

Pronunciation[edit]

Noun[edit]

Usage notes[edit]

Coordinate terms[edit]

Derived terms[edit]

Translations[edit]

Adjective[edit]

Synonyms[edit]

Antonyms[edit]

Derived terms[edit]

Translations[edit]

Verb[edit]

Derived terms[edit]

Translations[edit]

Etymology 2[edit]

Noun[edit]

German[edit]

Etymology[edit]

Pronunciation[edit]

Adjective[edit]

Further reading[edit]

Middle French[edit]

Etymology[edit]

Noun[edit]

References[edit]

In normal speech, mean and average both mean the same thing.

In a math sense, they are identical. However, average can also mean «normal» and mean can also mean «rude» or «the definition of something.»

@ghetty2223 they are the same in math. But if not in math then ‘average’ is like “normal” and ‘mean’ is like “rude, aggressive”. In math they both are adding and then dividing by how many numbers.“12 is the mean (average) of 11,12,and 13” that is like 11+12+13=36, the 36/3=12.

They both mean the same thing.The average of 10, 14 is 12The mean of 10, 14 is 12 And here’s a math joke! “My teacher called me average, how mean!”

In a math sense, they are identical.

However, average can also mean «normal» and mean can also mean «rude» or «the definition of something.»

@ghetty2223 they are the same in math. But if not in math then ‘average’ is like “normal” and ‘mean’ is like “rude, aggressive”.
In math they both are adding and then dividing by how many numbers.
“12 is the mean (average) of 11,12,and 13” that is like 11+12+13=36, the 36/3=12.

They both mean the same thing.
The average of 10, 14 is 12
The mean of 10, 14 is 12

And here’s a math joke!
“My teacher called me average, how mean!”