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 for On an average
From The Collaborative International Dictionary of English v.0.48 :

  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, port dues. The first meaning was perhaps
     the service of carting a feudal lord's wheat, then charge for
     carriage, the contribution towards loss of things carried, in
     proportion to the amount of each person's property. Cf.
     Aver, n., Avercorn, Averpenny.]
     1. (OLd Eng. Law) 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.
        [1913 Webster]
     2. [Cf. F. avarie damage to ship or cargo.] (Com.)
        (a) A tariff or duty on goods, etc. [Obs.]
        (b) Any charge in addition to the regular charge for
            freight of goods shipped.
        (c) A contribution to a loss or charge which has been
            imposed upon one of several for the general benefit;
            damage done by sea perils.
        (d) The equitable and proportionate distribution of loss
            or expense among all interested.
            [1913 Webster]
     General average, a contribution made, by all parties
        concerned in a sea adventure, toward a loss occasioned by
        the voluntary sacrifice of the property of some of the
        parties in interest for the benefit of all. It is called
        general average, because it falls upon the gross amount of
        ship, cargo, and freight at risk and saved by the
        sacrifice. --Kent.
     Particular average signifies the damage or partial loss
        happening to the ship, or cargo, or freight, in
        consequence of some fortuitous or unavoidable accident;
        and it is borne by the individual owners of the articles
        damaged, or by their insurers.
     Petty averages are sundry small charges, which occur
        regularly, and are necessarily defrayed by the master in
        the usual course of a voyage; such as port charges, common
        pilotage, and the like, which formerly were, and in some
        cases still are, borne partly by the ship and partly by
        the cargo. In the clause commonly found in bills of
        lading, "primage and average accustomed," average means a
        kind of composition established by usage for such charges,
        which were formerly assessed by way of average. --Arnould.
        --Abbott. --Phillips.
        [1913 Webster]
     3. A mean proportion, medial sum or quantity, made out of
        unequal sums or quantities; an arithmetical mean. Thus, if
        A loses 5 dollars, B 9, and C 16, the sum is 30, and the
        average 10.
        [1913 Webster]
     4. Any medial estimate or general statement derived from a
        comparison of diverse specific cases; a medium or usual
        size, quantity, quality, rate, etc. "The average of
        sensations." --Paley.
        [1913 Webster]
     5. pl. In the English corn trade, the medial price of the
        several kinds of grain in the principal corn markets.
        [1913 Webster]
     On an average, taking the mean of unequal numbers or
        [1913 Webster]

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