Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 n. Mathematics A number that typifies a set of numbers of which it is a function.
 n. Mathematics See arithmetic mean.
 n. An intermediate level or degree: near the average in size.
 n. The usual or ordinary kind or quality: Although the wines vary, the average is quite good.
 n. Sports The ratio of a team's or player's successful performances such as wins, hits, or goals, divided by total opportunities for successful performance, such as games, times at bat, or shots: finished the season with a .500 average; a batting average of .274.
 n. Law The loss of a ship or cargo, caused by damage at sea.
 n. Law The incurrence of damage or loss of a ship or cargo at sea.
 n. Law The equitable distribution of such a loss among concerned parties.
 n. Law A charge incurred through such a loss.
 n. Nautical Small expenses or charges that are usually paid by the master of a ship.
 adj. Mathematics Of, relating to, or constituting an average.
 adj. Being intermediate between extremes, as on a scale: a player of average ability.
 adj. Usual or ordinary in kind or character: a poll of average people; average eyesight.
 adj. Assessed in accordance with the law of averages.
 transitive v. Mathematics To calculate the average of: average a set of numbers.
 transitive v. To do or have an average of: averaged three hours of work a day.
 transitive v. To distribute proportionately: average one's income over four years so as to minimize the tax rate.
 intransitive v. To be or amount to an average: Some sparrows are six inches long, but they average smaller. Our expenses averaged out to 45 dollars per day.
 average down To purchase shares of the same security at successively lower prices in order to reduce the average price of one's position.
 average up To purchase shares of the same security at successively higher prices in order to achieve a larger position at an average price that is lower than the current market value.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. Customs duty or similar charge payable on transported goods.
 n. Proportional or equitable distribution of financial expense.
 n. The arithmetic mean.
 n. Any measure of central tendency, especially any mean, the median, or the mode.
 n. An indication of a player's ability calculated from his scoring record, etc.
 adj. Constituting or relating to the average.
 adj. Neither very good nor very bad; rated somewhere in the middle of all others in the same category.
 adj. Typical.
 adj. Not outstanding, not good, banal; bad or poor.
 v. To compute the arithmetic mean of.
 v. Over a period of time or across members of a population, to have or generate a mean value of.
from the GNU version of the Collaborative International Dictionary of English
 n. That service which a tenant owed his lord, to be done by the work beasts of the tenant, as the carriage of wheat, turf, etc.
 n.
 n. A tariff or duty on goods, etc.
 n. Any charge in addition to the regular charge for freight of goods shipped.
 n. A contribution to a loss or charge which has been imposed upon one of several for the general benefit; damage done by sea perils.
 n. The equitable and proportionate distribution of loss or expense among all interested.
 n. A mean proportion, medial sum or quantity, made out of unequal sums or quantities; an arithmetical mean.
 n. Any medial estimate or general statement derived from a comparison of diverse specific cases; a medium or usual size, quantity, quality, rate, etc.
 n. In the English corn trade, the medial price of the several kinds of grain in the principal corn markets.
 adj. Pertaining to an average or mean; medial; containing a mean proportion; of a mean size, quality, ability, etc.; ordinary; usual
 adj. According to the laws of averages.
 transitive v. To find the mean of, when sums or quantities are unequal; to reduce to a mean.
 transitive v. To divide among a number, according to a given proportion.
 transitive v. To do, accomplish, get, etc., on an average.
 intransitive v. To form, or exist in, a mean or medial sum or quantity; to amount to, or to be, on an average
from The Century Dictionary and Cyclopedia
 n. In old law, a kind of service owed by tenants to their superior.
 n. A duty or tax upon goods.
 n. A small charge payable by the shippers of goods to the master of the ship, over and above the freight, for his care of the goods. Hence the clause, in bills of lading, “paying so much freight, with primage and average accustomed.”
 n. A small charge paid by the master on account of the ship and cargo, such as pilotage, towage, etc.: called more specifically petty average.
 n. A loss, or the sum paid on account of a loss (such as that of an anchor), when the general safety is not in question, and which falls on the owner of the particular property lost: called more specifically particular average.
 n. A contribution made by the owners of a ship's freight and cargo, in proportion to their several interests, to make good a loss that has been sustained or an expense incurred for the general safety of the ship and cargo.
 n. A sum or quantity intermediate to a number of different sums or quantities, obtained by adding them together and dividing the result by the number of quantities added; an arithmetical mean proportion. Thus, if four persons lose respectively $10, $20, $30, and $40, the average loss by the four is $25.
 n. Any medial amount, estimate, or general statement based on a comparison of a number of diverse specific cases; a medium.
 To find the arithemetical mean of, as unequal sums or quantities; reduce to a mean.
 To result in, as an arithmetical mean term; amount to, as a mean sum or quantity: as, wheat averages 56 pounds to the bushel.
 To divide among a number proportionally; divide the total amount of by the number of equal shares: as, to average a loss.
 n. The stubble and grass left in cornfields after harvest.
 n. A mode of estimating, by comparison, the strength or weakness of a billiard play.
 n. In cricket: The aggregate number of runs a batsman has scored, divided by the number of his completed innings.
 n. The aggregate number of runs scored from a bowler, divided by the number of batsmen he has ‘dismissed.’
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 adj. 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)
 adj. around the middle of a scale of evaluation
 v. amount to or come to an average, without loss or gain
 adj. lacking special distinction, rank, or status; commonly encountered
 adj. approximating the statistical norm or average or expected value
 n. (sports) the ratio of successful performances to opportunities
 v. compute the average of
 n. an intermediate scale value regarded as normal or usual
 v. achieve or reach on average
 n. a statistic describing the location of a distribution
 adj. relating to or constituting the most frequent value in a distribution
 adj. lacking exceptional quality or ability
Etymologies
from The American Heritage® Dictionary of the English Language, 4th Edition
from Wiktionary, Creative Commons Attribution/ShareAlike License
Examples

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 twentyfold.

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.

_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.

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

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

The term average originally meant what is now distinguished as general average; and the expression
Encyclopaedia Britannica, 11th Edition, Volume 3, Part 1, Slice 1 "Austria, Lower" to "Bacon"

What "Average" means  Many of us use the term average when we discuss metrics, this is a great primer to understand the term better.

The numbers are even higher in places like Chicago, where the average is almost $42,000.
Akito Yoshikane: The Pension Pinch: PublicSector Unions Grapple With Rhetoric and Rollbacks

The longterm average is about 80%, and with current growth rates we should be there in a year.

Once decided that idea needs to be written, not once but rewritten several times (my average is around six drafts per story)
brtom commented on the word average
O such themes  equalities! O divine average!
Whitman, "Starting from Paumanok"
January 9, 2008