Difference between revisions of "Manuals/calci/GEOMEAN"

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<div style="font-size:30px">'''GEOMEAN(n1,n2,…)'''</div><br/>
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<div style="font-size:30px">'''GEOMEAN()'''</div><br/>
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*<math>n1,n2</math> are the positive real numbers.
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*Parameters are any set of  positive real numbers.
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**GEOMEAN(),Returns the geometric mean.
 +
 
 
==Description==
 
==Description==
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*This function gives the geometric mean of an array or references.
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*This function gives the Geometric Mean of an array or references.
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*For example it is used to calculate average rate of growth of human population.  
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*For example, it is used to calculate average rate of growth of human population.  
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*The geometric mean of two numbers, is  the square root of their product and the geometric mean of the three numbers is the cube root of their product.  
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*The Geometric Mean of two numbers is, the square root of their product.
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*So the geometric mean of n numbers is defined as the nth root of the product of the numbers.
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*The Geometric Mean of the three numbers is, the cube root of their product.  
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*In GEOMEAN(n1,n2...)n1,n2.., are positive real numbers and n1 is required. n2,n3.. are optional.
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*So the geometric mean of <math>n</math> numbers is defined as the <math>n^{th}</math> root of the product of the numbers.
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*The  arguments  can be numbers ,names, arrays or references that contain numbers.  
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*In <math>GEOMEAN()</math>, Parameters are any set of positive real numbers and first parameter is required. From second parameters are optional.
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*The  arguments  can be numbers,names,arrays or references that contain numbers.  
 
*Also we can directly use logical values and text representations of numbers.
 
*Also we can directly use logical values and text representations of numbers.
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*The values are ignored when the argument contains logical values or empty cells.  
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*The values are ignored, when the argument contains logical values or empty cells.  
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*The geometric and arithmetic means are equal when all the numbers in the given set are equal,otherwise the geometric mean of a data set is less than the data set's arithmetic mean.
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*The Geometric and Arithmetic Means are equal, when all the numbers in the given set are equal, otherwise the Geometric Mean of a data set is less than the data set's Arithmetic Mean.
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*The geometric mean of a data set {a1,a2 ...,an} is given by:
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*The geometric mean of a data set <math>[a_1,a_2,...a_n]</math> is given by:
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[PI(){i=1 to n} ai] ^{1/n} = sqrt[n]{a1, a2 ... an}.
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<math>({\prod_{i=1}^n a_i})^{\frac{1}{n}} = \sqrt[n]{a_1, a_2 ... a_n}</math>
 
*This function will give the result as error when  
 
*This function will give the result as error when  
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#Any one of the argument is nonnumeric
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1.Any one of the argument is non-numeric
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#Any one value<=0
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2.Any one <math>value \le 0</math>
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#Any one of the references cannot be translated in to numbers.
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3.Any one of the references cannot be translated in to numbers.
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 +
==ZOS==
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*The syntax is to calculate GEOMEAN in ZOS is <math>GEOMEAN()</math>.
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**Parameters are any set of positive real numbers.
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*For e.g.,GEOMEAN(1,2,3,4,5),GEOMEAN(11.5..20.5..0.5)
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{{#ev:youtube|me2sEpY6LD4|280|center|Geometric Mean}}
  
 
==Examples==
 
==Examples==
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GEOMEAN(3,27)=9
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#=GEOMEAN(3,27) = 9
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GEOMEAN(2,4,8)=4
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#=GEOMEAN(2,4,8) = 3.9999999999999996
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GEOMEAN(3,5,8,10,12)=6.786916380543178
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#=GEOMEAN(3,5,8,10,12) = 6.786916380543178
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GEOMEAN(-2,32)=NAN, because the value is<0.
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#=GEOMEAN(-2,32) = #N/A (NUMBER > 0 REQUIRED)
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==Related Videos==
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{{#ev:youtube|s-DXD1W48A8|280|center|Geometric Mean}}
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==See Also==
 
==See Also==
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*[[Manuals/calci/AVERAGE  | AVERAGE ]]
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*[[Manuals/calci/SUM  | SUM ]]
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*[[Manuals/calci/TRIMMEAN |TRIMMEAN ]]
  
 
==References==
 
==References==
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[http://en.wikipedia.org/wiki/Gamma_distribution| Gamma Distribution]*
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*[http://en.wikipedia.org/wiki/Geometric_mean| Geometric Mean]
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 +
 
 +
 
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*[[Z_API_Functions | List of Main Z Functions]]
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*[[ Z3 |  Z3 home ]]

Latest revision as of 04:01, 12 August 2020

GEOMEAN()


  • Parameters are any set of positive real numbers.
    • GEOMEAN(),Returns the geometric mean.

Description

  • This function gives the Geometric Mean of an array or references.
  • For example, it is used to calculate average rate of growth of human population.
  • The Geometric Mean of two numbers is, the square root of their product.
  • The Geometric Mean of the three numbers is, the cube root of their product.
  • So the geometric mean of numbers is defined as the root of the product of the numbers.
  • In , Parameters are any set of positive real numbers and first parameter is required. From second parameters are optional.
  • The arguments can be numbers,names,arrays or references that contain numbers.
  • Also we can directly use logical values and text representations of numbers.
  • The values are ignored, when the argument contains logical values or empty cells.
  • The Geometric and Arithmetic Means are equal, when all the numbers in the given set are equal, otherwise the Geometric Mean of a data set is less than the data set's Arithmetic Mean.
  • The geometric mean of a data set is given by:

  • This function will give the result as error when
1.Any one of the argument is non-numeric
2.Any one 
3.Any one of the references cannot be translated in to numbers.

ZOS

  • The syntax is to calculate GEOMEAN in ZOS is .
    • Parameters are any set of positive real numbers.
  • For e.g.,GEOMEAN(1,2,3,4,5),GEOMEAN(11.5..20.5..0.5)
Geometric Mean

Examples

  1. =GEOMEAN(3,27) = 9
  2. =GEOMEAN(2,4,8) = 3.9999999999999996
  3. =GEOMEAN(3,5,8,10,12) = 6.786916380543178
  4. =GEOMEAN(-2,32) = #N/A (NUMBER > 0 REQUIRED)

Related Videos

Geometric Mean

See Also

References


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