A previous node suggested the following:
Add all the numbers, then divide by the number of numbers. Average.

Technically, this is correct, but we should note that the mean for a sample is usually considered slightly differently. Sure, it is still the sum of values divided by the number of cases. However, given degrees of freedom problems, one must subtract 1 from the number of cases when using sample means in order to arrive at an unbiased value. When used correctly, the mean is what is known as BLUE, which is the Best Linear Unbiased Estimator.

In statistics, one type of average, also known as arithmetic mean (to differentiate it from geometric mean). In any numerical sample, the (arithmetic) mean is derived by dividing the sum by the number of members in the sample. Thus, in the series 2,3,4,5,5,5,7,8,9,9, the mean is 5.7, because the sum is 57 and there are 10 numbers in the sample ( 57 / 10 = 5.7 ).

Mean (?), v. t. [imp. & p. p. Meant (?); p. pr. & vb. n. Meaning.] [OE. menen, AS. m&aemac;nan to recite, tell, intend, wish; akin to OS. m&emac;nian to have in mind, mean, D. meenen, G. meinen, OHG. meinan, Icel. meina, Sw. mena, Dan. mene, and to E. mind. . See Mind, and cf. Moan.]

1.

To have in the mind, as a purpose, intention, etc.; to intend; to purpose; to design; as, what do you mean to do ?

What mean ye by this service ? Ex. xii. 26.

Ye thought evil against me; but God meant it unto good. Gen. 1. 20.

I am not a Spaniard To say that it is yours and not to mean it. Longfellow.

2.

To signify; to indicate; to import; to denote.

What mean these seven ewe lambs ? Gen. xxi. 29.

Go ye, and learn what that meneth. Matt. ix. 13.

Mean, v. i.

To have a purpose or intention.

[Rare, except in the phrase to mean well, or ill.]

Shak.

Mean (?), a. [Compar. Meaner (?); superl. Meanest.] [OE. mene, AS. mne wicked; akin to man, a., wicked, n., wickedness, OS. mn wickedness, OHG. mein, G. meineid perjury, Icel. mein harm, hurt, and perh. to AS. gemne common, general, D. gemeen, G. gemein, Goth. gam�xa0;ins, and L. communis. The AS. gemne prob. influenced the meaning.]

1.

Destitute of distinction or eminence; common; low; vulgar; humble.

"Of mean parentage."

Sir P. Sidney.

The mean man boweth down, and the great man humbleth himself. Is. ii. 9.

2.

Wanting dignity of mind; low-minded; base; destitute of honor; spiritless; as, a mean motive.

Can you imagine I so mean could prove, To save my life by changing of my love ? Dryden.

3.

Of little value or account; worthy of little or no regard; contemptible; despicable.

The Roman legions and great Caesar found Our fathers no mean foes. J. Philips.

4.

Of poor quality; as, mean fare.

5.

Penurious; stingy; close-fisted; illiberal; as, mean hospitality.

Mean is sometimes used in the formation of compounds, the sense of which is obvious without explanation; as, meanborn, mean-looking, etc.

Syn. -- Base; ignoble; abject; beggarly; wretched; degraded; degenerate; vulgar; vile; servile; menial; spiritless; groveling; slavish; dishonorable; disgraceful; shameful; despicable; contemptible; paltry; sordid. See Base.

Mean, a. [OE. mene, OF. meiien, F. moyen, fr. L. medianus that is in the middle, fr. medius; akin to E. mid. See Mid.]

1.

Occupying a middle position; middle; being about midway between extremes.

Being of middle age and a mean stature. Sir. P. Sidney.

2.

Intermediate in excellence of any kind.

According to the fittest style of lofty, mean, or lowly. Milton.

3. Math.

Average; having an intermediate value between two extremes, or between the several successive values of a variable quantity during one cycle of variation; as, mean distance; mean motion; mean solar day.

Mean distance (of a planet from the sun) Astron., the average of the distances throughout one revolution of the planet, equivalent to the semi-major axis of the orbit. -- Mean error Math. Phys., the average error of a number of observations found by taking the mean value of the positive and negative errors without regard to sign. -- Mean-square error, ∨ Error of the mean square Math. Phys., the error the square of which is the mean of the squares of all the errors; -- called also, especially by European writers, mean error. -- Mean line. Crystallog. Same as Bisectrix. -- Mean noon, noon as determined by mean time. -- Mean proportional (between two numbers) Math., the square root of their product. -- Mean sun, a fictitious sun supposed to move uniformly in the equator so as to be on the meridian each day at mean noon. -- Mean time, time as measured by an equable motion, as of a perfect clock, or as reckoned on the supposition that all the days of the year are of a mean or uniform length, in contradistinction from apparent time, or that actually indicated by the sun, and from sidereal time, or that measured by the stars.

Mean, n.

1.

That which is mean, or intermediate, between two extremes of place, time, or number; the middle point or place; middle rate or degree; mediocrity; medium; absence of extremes or excess; moderation; measure.

But to speak in a mean, the virtue of prosperity is temperance; the virtue of adversity is fortitude. Bacon.

There is a mean in all things. Dryden.

The extremes we have mentioned, between which the wellinstracted Christian holds the mean, are correlatives. I. Taylor.

2. Math.

A quantity having an intermediate value between several others, from which it is derived, and of which it expresses the resultant value; usually, unless otherwise specified, it is the simple average, formed by adding the quantities together and dividing by their number, which is called an arithmetical mean. A geometrical mean is the square root of the product of the quantities.

3.

That through which, or by the help of which, an end is attained; something tending to an object desired; intermediate agency or measure; necessary condition or coagent; instrument.

Their virtuous conversation was a mean to work the conversion of the heathen to Christ. Hooker.

You may be able, by this mean, to review your own scientific acquirements. Coleridge.

Philosophical doubt is not an end, but a mean. Sir W. Hamilton.

⇒ In this sense the word is usually employed in the plural form means, and often with a singular attribute or predicate, as if a singular noun.

By this means he had them more at vantage. Bacon.

What other means is left unto us. Shak.

4. pl.

Hence: Resources; property, revenue, or the like, considered as the condition of easy livelihood, or an instrumentality at command for effecting any purpose; disposable force or substance.

5. Mus.

A part, whether alto or tenor, intermediate between the soprano and base; a middle part.

[Obs.]

The mean is drowned with your unruly base. Shak.

6.

Meantime; meanwhile.

[Obs.]

Spenser.

7.

A mediator; a go-between.

[Obs.]

Piers Plowman.

He wooeth her by means and by brokage. Chaucer.

By all means, certainly; without fail; as, go, by all means. -- By any means, in any way; possibly; at all.

If by any means I might attain to the resurrection of the dead. Phil. iii. ll.

-- By no means, ∨ By no manner of means, not at all; certainly not; not in any degree.

The wine on this side of the lake is by no means so good as that on the other. Addison.

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