geometrical mean

Mean \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.
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            But to speak in a mean, the virtue of prosperity is
            temperance; the virtue of adversity is fortitude.
                                                  --Bacon.
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            There is a mean in all things.        --Dryden.
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            The extremes we have mentioned, between which the
            wellinstracted Christian holds the mean, are
            correlatives.                         --I. Taylor.
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   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
      nth root of the product of the n quantities being
      averaged.
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   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.
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            Their virtuous conversation was a mean to work the
            conversion of the heathen to Christ.  --Hooker.
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            You may be able, by this mean, to review your own
            scientific acquirements.              --Coleridge.
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            Philosophical doubt is not an end, but a mean. --Sir
                                                  W. Hamilton.
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   Note: 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.
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               By this means he had them more at vantage.
                                                  --Bacon.
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               What other means is left unto us.  --Shak.
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   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.
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            Your means are very slender, and your waste is
            great.                                --Shak.
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   5. (Mus.) A part, whether alto or tenor, intermediate between
      the soprano and base; a middle part. [Obs.]
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            The mean is drowned with your unruly base. --Shak.
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   6. Meantime; meanwhile. [Obs.] --Spenser.
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   7. A mediator; a go-between. [Obs.] --Piers Plowman.
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            He wooeth her by means and by brokage. --Chaucer.
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   {By all means}, certainly; without fail; as, go, by all
      means.

   {By any means}, in any way; possibly; at all.
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            If by any means I might attain to the resurrection
            of the dead.                          --Phil. iii.
                                                  ll.
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   {By no means}, or {By no manner of means}, not at all;
      certainly not; not in any degree.
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            The wine on this side of the lake is by no means so
            good as that on the other.            --Addison.
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