# Mean vs. Meen - What's the difference?

### Mean

In mathematics, mean has several different definitions depending on the context. In probability and statistics, population mean and expected value are used synonymously to refer to one measure of the central tendency either of a probability distribution or of the random variable characterized by that distribution. In the case of a discrete probability distribution of a random variable X, the mean is equal to the sum over every possible value weighted by the probability of that value; that is, it is computed by taking the product of each possible value x of X and its probability P(x), and then adding all these products together, giving μ = ∑ x P ( x ) {\displaystyle \mu =\sum xP(x)} . An analogous formula applies to the case of a continuous probability distribution. Not every probability distribution has a defined mean; see the Cauchy distribution for an example. Moreover, for some distributions the mean is infinite: for example, when the probability of the value 2 n {\displaystyle 2^{n}} is 1 2 n {\displaystyle {\tfrac {1}{2^{n}}}} for n = 1, 2, 3, .... For a data set, the terms arithmetic mean, mathematical expectation, and sometimes average are used synonymously to refer to a central value of a discrete set of numbers: specifically, the sum of the values divided by the number of values. The arithmetic mean of a set of numbers x1, x2, ..., xn is typically denoted by x ¯ {\displaystyle {\bar {x}}} , pronounced "x bar". If the data set were based on a series of observations obtained by sampling from a statistical population, the arithmetic mean is termed the sample mean (denoted x ¯ {\displaystyle {\bar {x}}} ) to distinguish it from the population mean (denoted μ {\displaystyle \mu } or μ x {\displaystyle \mu _{x}} ). For a finite population, the population mean of a property is equal to the arithmetic mean of the given property while considering every member of the population. For example, the population mean height is equal to the sum of the heights of every individual divided by the total number of individuals. The sample mean may differ from the population mean, especially for small samples. The law of large numbers dictates that the larger the size of the sample, the more likely it is that the sample mean will be close to the population mean. Outside probability and statistics, a wide range of other notions of "mean" are often used in geometry and analysis; examples are given below.

1. Pronunciation

## 1. Pronunciation

• enPR: mēn, IPA(key): /miːn/
• Rhymes: -iːn
• Homophone: mien

## 2. Etymology 1

From Middle English menen (to intend; remember; lament; comfort), from Old English mǣnan (to mean, signify; lament), from Proto-Germanic *mainijaną (to mean, think; lament), from Proto-Indo-European *meyn- (to think). Germanic cognates include West Frisian miene (to deem, think) (Old Frisian mēna (signify)), Dutch menen (to believe, think, mean) (Middle Dutch menen (think, intend)), German meinen (to think, mean, believe), Old Saxon mēnian. Indo-European cognates include Old Irish mían (wish, desire) and Polish mienić (signify, believe). Related to moan.

### 2.1. Verb

mean (third-person singular simple present means, present participle meaning, simple past and past participle meant)

1. To intend.
1. (transitive) To intend, to plan (to do); to have as one's intention. [from 8th c.]
2. (intransitive) To have intentions of a given kind. [from 14th c.]
3. (transitive, usually in passive) To intend (something) for a given purpose or fate; to predestine. [from 16th c.]
2. To convey meaning.
1. (transitive) To convey (a given sense); to signify, or indicate (an object or idea). [from 8th c.]
2. (transitive) Of a word, symbol etc: to have reference to, to signify. [from 8th c.]
• A term should be included if it's likely that someone would run across it and want to know what it means. This in turn leads to the somewhat more formal guideline of including a term if it is attested and idiomatic.
3. (transitive) To have conviction in (something said or expressed); to be sincere in (what one says). [from 18th c.]
4. (transitive) To result in; to bring about. [from 19th c.]
5. (transitive) To be important (to). [from 19th c.]

#### 2.1.1. Synonyms

• (convey, signify, indicate): convey, indicate, signify
• (want or intend to convey): imply, mean to say
• (intend; plan on doing): intend
• (have conviction in what one says): be serious
• (have intentions of a some kind):

### 2.2. Verb

mean (third-person singular simple present means, present participle meaning, simple past and past participle meaned)

1. (Ireland, Britain regional) To lament.
• c. 1385, William Langland, Piers Plowman, III:
Thanne morned Mede · and mened hire to the kynge / To haue space to speke · spede if she myȝte.
• 1560 (1677), Spottiswood Hist. Ch. Scot. iii. (1677), page 144:
They were forced to mean our estate to the Queen of England.
• 1803, Sir Walter Scott, Minstrelsy of the Scottish Border, page 276:
If you should die for me, sir knight, There's few for you will meane, [...]
• 1845, Wodrow Society Select Biographies:
All the tyme of his sickness he never said, "Alace!" or meaned any pain, whilk was marvellous. Never man died in greater peace of mind or body.

## 3. Etymology 2

From Middle English mene, imene, from Old English mǣne, ġemǣne (common, public, general, universal), from Proto-Germanic *gamainiz (common), from Proto-Indo-European *mey- (to change, exchange, share). Cognate with West Frisian mien (general, universal), Dutch gemeen (common, mean), German gemein (common, mean, nasty), Gothic 𐌲𐌰𐌼𐌰𐌹𐌽𐍃 (gamains, common, unclean), Latin commūnis (shared, common, general) (Old Latin comoinem).

mean (comparative meaner, superlative meanest)

1. (obsolete) Common; general.
• Ivanhoe (1952 film)
Prince John: "Your foe has bloodied you, sir knight. Will you concede defeat? You fight too well to die so mean a death. Will you not throw in your lot with me instead?
Ivanhoe: "That would be an even meaner death, Your Grace."
2. Of a common or low origin, grade, or quality; common; humble.
3. Low in quality or degree; inferior; poor; shabby.
4. Without dignity of mind; destitute of honour; low-minded; spiritless; base.
a mean motive
• Dryden
Can you imagine I so mean could prove, / To save my life by changing of my love?
5. Of little value or account; worthy of little or no regard; contemptible; despicable.
• J. Philips
The Roman legions and great Caesar found / Our fathers no mean foes.
6. (chiefly Britain) Ungenerous; stingy, tightfisted; North American English: cheap; formal: niggardly, penurious, miserly.
7. Disobliging; pettily offensive or unaccommodating; small.
8. Selfish; acting without consideration of others; unkind.
9. Causing or intending to cause intentional harm; bearing ill will towards another; cruel; malicious.
10. Powerful; fierce; harsh; damaging.
11. Accomplished with great skill; deft; hard to compete with.
12. (informal, often childish) Difficult, tricky.

#### 3.1.1. Synonyms

• (causing or intending to cause intentional harm): cruel, malicious, nasty, spiteful
• (low-minded; acting without consideration of others): base, ignoble, selfish, unkind, vile
• (powerful): damaging, fierce, harsh, strong
• (accomplished with great skill; deft; hard to compete with): deft, skilful (UK), skillful (US), top-notch
• (inferior): cheap, grotty (slang), inferior, low-quality, naff (UK slang), rough and ready, shoddy, tacky (informal)

#### 3.1.2. Antonyms

• (low-minded; acting without consideration of others): lofty, noble, honorable

## 4. Etymology 3

From Middle English meene, from Old French meien (French moyen), Late Latin mediānus (that is in the middle, middle), from Latin medius (middle). Cognate with mid. For the musical sense, compare the cognate Italian mezzano.

mean (not comparable)

1. Having the mean (see noun below) as its value.
2. (obsolete) Middling; intermediate; moderately good, tolerable.
• , II.ii.2:
I have declared in the causes what harm costiveness hath done in procuring this disease; if it be so noxious, the opposite must needs be good, or mean at least, as indeed it is […].
• Sir Philip Sidney
being of middle age and a mean stature
• Milton
according to the fittest style of lofty, mean, or lowly

### 4.2. Noun

mean (plural means)

1. (now chiefly in the plural) A method or course of action used to achieve some result. [from 14th c.]
• 1603, John Florio, translating Michel de Montaigne, Essays, II.5:
To say truth, it is a meane full of uncertainty and danger.
• Coleridge
You may be able, by this mean, to review your own scientific acquirements.
• Sir W. Hamilton
Philosophical doubt is not an end, but a mean.
• 2011, "Rival visions", The Economist, 14 Apr 2011:
Mr Obama produced an only slightly less ambitious goal for deficit reduction than the House Republicans, albeit working from a more forgiving baseline: $4 trillion over 12 years compared to$4.4 trillion over 10 years. But the means by which he would achieve it are very different.
2. (obsolete, in the singular) An intermediate step or intermediate steps.
• a. 1563, Thomas Harding, "To the Reader", in The Works of John Jewel (1845 ed.)
Verily in this treatise this hath been mine only purpose; and the mean to bring the same to effect hath been such as whereby I studied to profit wholesomely, not to please delicately.
• 1606, The Trials of Robert Winter, Thomas Winter, Guy Fawkes, John Grant, Ambrose Rookwood, Rob. Keyes, Thomas Bates, and Sir Everard Digby, at Westminster, for High Treason, being Conspirators in the Gunpowder-Plot
That it was lawful and meritorious to kill and destroy the king, and all the said hereticks. — The mean to effect it, they concluded to be, that, 1. The king, the queen, the prince, the lords spiritual and temporal, the knights and burgoses of the parliament, should be blown up with powder. 2. That the whole royal issue male should be destroyed. S. That they would lake into their custody Elizabeth and Mary the king's daughters, and proclaim the lady Elizabeth queen. 4. That they should feign a Proclamation in the name of Elizabeth, in which no mention should be made of alteration of religion, nor that they were parties to the treason, until they had raised power to perform the same; and then to proclaim, all grievances in the kingdom should be reformed.
• a. 1623, John Webster, The Duchess of Malfi
Apply desperate physic: / We must not now use balsamum, but fire, / The smarting cupping-glass, for that's the mean / To purge infected blood, such blood as hers.
3. Something which is intermediate or in the middle; an intermediate value or range of values; a medium. [from 14th c.]
• 1875, William Smith and Samuel Cheetham, editors, A Dictionary of Christian Antiquities, Little, Brown and Company, volume 1, page 10, s.v. Accentus Ecclesiasticus,
It presents a sort of mean between speech and song, continually inclining towards the latter, never altogether leaving its hold on the former; it is speech, though always attuned speech, in passages of average interest and importance; it is song, though always distinct and articulate song, in passages demanding more fervid utterance.
4. (music, now historical) The middle part of three-part polyphonic music; now specifically, the alto part in polyphonic music; an alto instrument. [from 15th c.]
• 1624, John Smith, Generall Historie, in Kupperman 1988, page 147:
Of these [rattles] they have Base, Tenor, Countertenor, Meane, and Treble.
5. (statistics) The average of a set of values, calculated by summing them together and dividing by the number of terms; the arithmetic mean. [from 15th c.]
6. (mathematics) Any function of multiple variables that satisfies certain properties and yields a number representative of its arguments; or, the number so yielded; a measure of central tendency.
• 1997, Angus Deaton, The Analysis of Household Surveys: A Microeconometric Approach to Development Policy,[2] World Bank Publications, ISBN 9780801852541, page 51:
Note that (1.41) is simply the probability-weighted mean without any explicit allowance for the stratification; each observation is weighted by its inflation factor and the total divided by the total of the inflation factors for the survey.
• 2002, Clifford A. Pickover, The Mathematics of Oz: Mental Gymnastics from Beyond the Edge,[3] Cambridge University Press, ISBN 9780521016780, page 246:
Luckily, even though the arithmetic mean is unusable, both the harmonic and geometric means settle to precise values as the amount of data increases.
• 2003, P. S. Bullen, Handbook of Means and Their Inequalities,[4] Springer, ISBN 978-1-4020-1522-9, page 251:
The generalized power means include power means, certain Gini means, in particular the counter-harmonic means.
7. (mathematics) Either of the two numbers in the middle of a conventionally presented proportion, as 2 and 3 in 1:2=3:6.
• 1825, John Farrar, translator, An Elementary Treatise on Arithmetic by Silvestre François Lacroix, third edition, page 102,
...if four numbers be in proportion, the product of the first and last, or of the two extremes, is equal to the product of the second and third, or of the two means.
• 1999, Dawn B. Sova, How to Solve Word Problems in Geometry, McGraw-Hill, ISBN 007134652X, page 85,
Using the means-extremes property of proportions, you know that the product of the extremes equals the product of the means. The ratio t/4 = 5/2 can be rewritten as t:4 = 5:2, in which the extremes are t and 2, and the means are 4 and 5.
• 2007, Carolyn C. Wheater, Homework Helpers: Geometry, Career Press, ISBN 1564147215, page 99,
In ${\displaystyle {\frac {18}{27}}={\frac {2}{3}}}$, the product of the means is ${\displaystyle 2\cdot 27}$, and the product of the extremes is ${\displaystyle 18\cdot 3}$. Both products are 54.

#### 4.2.1. Hypernyms

• (statistics): measure of central tendency, measure of location, sample statistic

#### 4.2.2. Coordinate terms

• (statistics): median, mode

• “mean” at OneLook Dictionary Search
• mean in The Century Dictionary, The Century Co., New York, 1911

## 6. Anagrams

• -mane, -nema, Amen, Eman, Enma, MENA, Mena, NAmE, NEMA, NMEA, amen, mane, mnae, name, namé, neam, ñame

• Rhymes: -eːn

## 2. Verb

meen

1. first-person singular present indicative of menen
2. imperative of menen

## 3. Anagrams

• mene, neem, neme