Definitions for geometric mean
geo·met·ric mean

Princeton's WordNetRate this definition:0.0 / 0 votes

1. geometric meannoun

   the mean of n numbers expressed as the n-th root of their product

WiktionaryRate this definition:0.0 / 0 votes

1. geometric meannoun

   A measure of central tendency of a set of n values computed by extracting the nth root of the product of the values.

WikipediaRate this definition:0.0 / 0 votes

1. Geometric mean

   In mathematics, the geometric mean is a mean or average which indicates a central tendency of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean is defined as the nth root of the product of n numbers, i.e., for a set of numbers a1, a2, ..., an, the geometric mean is defined as ( ∏ i = 1 n a i ) 1 n = a 1 a 2 ⋯ a n n {\displaystyle \left(\prod _{i=1}^{n}a_{i}\right)^{\frac {1}{n}}={\sqrt[{n}]{a_{1}a_{2}\cdots a_{n}}}} or, equivalently, as the arithmetic mean in logscale:

ChatGPTRate this definition:0.0 / 0 votes

1. geometric mean

   The geometric mean is a type of average or mean that is calculated by multiplying all the values in a set, and then taking the nth root of the product, where "n" is the total number of values. It is often used when dealing with quantities that grow exponentially or when comparing different items with very high or low values.

WikidataRate this definition:0.0 / 0 votes

1. Geometric mean

   In mathematics, the geometric mean is a type of mean or average, which indicates the central tendency or typical value of a set of numbers by using the product of their values. The geometric mean is defined as the nth root of the product of the numbers. For instance, the geometric mean of two numbers, say 2 and 8, is just the square root of their product; that is ²√2 × 8 = 4. As another example, the geometric mean of the three numbers 4, 1, and 1/32 is the cube root of their product, which is 1/2; that is ³√4 × 1 × 1/32 = ½ . A geometric mean is often used when comparing different items – finding a single "figure of merit" for these items – when each item has multiple properties that have different numeric ranges. For example, the geometric mean can give a meaningful "average" to compare two companies which are each rated at 0 to 5 for their environmental sustainability, and are rated at 0 to 100 for their financial viability. If an arithmetic mean was used instead of a geometric mean, the financial viability is given more weight because its numeric range is larger- so a small percentage change in the financial rating makes a much larger difference in the arithmetic mean than a large percentage change in environmental sustainability. The use of a geometric mean "normalizes" the ranges being averaged, so that no range dominates the weighting, and a given percentage change in any of the properties has the same effect on the geometric mean. So, a 20% change in environmental sustainability from 4 to 4.8 has the same effect on the geometric mean as a 20% change in financial viability from 60 to 72.

Matched Categories

1. • Mean
   • Statistics

How to pronounce geometric mean?

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Numerology

1. Chaldean Numerology

   The numerical value of geometric mean in Chaldean Numerology is: 4

2. Pythagorean Numerology

   The numerical value of geometric mean in Pythagorean Numerology is: 2

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=geometric mean
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Geometric_Mean
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Geometric_Mean
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=geometric mean