What is "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.

   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 nth root of the product of the n quantities being averaged.

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.

   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.

   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.

   Your means are very slender, and your waste is great.
   --Shak.

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, or 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.