Difference between revisions of "Manuals/calci/HARMEAN"

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<div style="font-size:30px">'''HARMEAN(n1,n2)'''</div><br/>
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<div style="font-size:30px">'''HARMEAN()'''</div><br/>
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*<math>n1</math> and <math>n2</math> are the positive real numbers.
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*Parameters are any set of positive real numbers.
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**HARMEAN(), returns values along an exponential trend.
 +
 
 
==Description==
 
==Description==
 
*This function gives the Harmonic Mean of a given set of numbers.
 
*This function gives the Harmonic Mean of a given set of numbers.
 
*Harmonic mean is used to calculate the average of a set of numbers.
 
*Harmonic mean is used to calculate the average of a set of numbers.
 
*The Harmonic mean is always the lowest mean.
 
*The Harmonic mean is always the lowest mean.
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*Normally Harmonic mean < geometric mean < Arithmetic mean.
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*Normally <math>Harmonic mean < Geometric mean < Arithmetic mean</math>
 
*Harmonic mean is defined as the reciprocal of the arithmetic mean by the reciprocals of a specified set of numbers.
 
*Harmonic mean is defined as the reciprocal of the arithmetic mean by the reciprocals of a specified set of numbers.
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*The harmonic mean of a positive real numbers <math>x1,x2,x3....xn > 0</math> is defined by :
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*The harmonic mean of a positive real numbers <math>x_1,x_2,x_3....x_n > 0</math> is defined by :
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<math>H=\frac {n}{(1/x1+1/x2+...+1/xn)} =
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<math>H=\frac {n}{(1/x_1+1/x_2+...+1/x_n)} </math>
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: \frac{n}{\sum{i=1}^{n} \frac{1}{xi}}</math>.
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ie
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*In HARMEAN(n1,n2,...) n1,n2.. are the positive real numbers, and here n1 is required.n2,n3..., are optional.
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:<math> H=\frac{n}{\sum_{i=1}^{n} \frac{1}{xi}}</math>.
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*In <math>HARMEAN(),</math> Parameters are any  positive real numbers, and here First Parameter is required. From the second parameter are optional.
 
*Also arguments can be numbers,names, arrays or references that contain numbers.  
 
*Also arguments can be numbers,names, arrays or references that contain numbers.  
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*We can give logical values and text representations of numbers directly. Suppose the arguments contains any text, logical values or empty cells like that values are ignored.
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*We can give logical values and text representations of numbers directly.
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*This will give the result as error when 1.the arguments with the error values or the referred text couldn't translated in to numbers.
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*Suppose the arguments contains any text, logical values or empty cells like that values are ignored.
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2.Also any data point<=0.
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*This will give the result as error when  
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1.The arguments with the error values or the referred text couldn't translated in to numbers.
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2.Also any data <math>point \le 0</math>.
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==ZOS==
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*The syntax is to calculate HARMEAN in ZOS is <math>HARMEAN()</math>.
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**Parameters are any set of positive real numbers.
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*For e.g.,HARMEAN(20..30,11..15,45.1..56.1..0.5)
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{{#ev:youtube|oHiCLVUJz-4|280|center|Harmonic Mean}}
  
 
==Examples==
 
==Examples==
  
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#HARMEAN(1,2,3,4,5)=2.18978102189781
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#=HARMEAN(1,2,3,4,5) = 2.18978102189781
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#HARMEAN(20,25,32,41)=27.4649361523969
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#=HARMEAN(20,25,32,41) = 27.4649361523969
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#HARMEAN(0.25,5.4,3.7,10.1,15.2)=1.0821913906985883                   
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#=HARMEAN(0.25,5.4,3.7,10.1,15.2) = 1.0821913906985883                   
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#HARMEAN(3,5,0,2)=NAN
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#=HARMEAN(3,5,0,2) = #N/A (NUMBER > 0 REQUIRED)
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#HARMEAN(1,-2,4)=NAN
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#=HARMEAN(1,-2,4) = #N/A (NUMBER > 0 REQUIRED)
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==Related Videos==
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{{#ev:youtube|X3nQMiBK9rc|280|center|Harmonic Mean}}
  
 
==See Also==
 
==See Also==
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*[[Manuals/calci/GEOMEAN  | GEOMEAN ]]
 
*[[Manuals/calci/GEOMEAN  | GEOMEAN ]]
  
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==References==
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[http://en.wikipedia.org/wiki/Harmonic_mean Harmonic mean]
  
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==References==
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[http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient| Correlation]
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*[[Z_API_Functions | List of Main Z Functions]]
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*[[ Z3 |   Z3 home ]]

Latest revision as of 05:03, 12 August 2020

HARMEAN()


  • Parameters are any set of positive real numbers.
    • HARMEAN(), returns values along an exponential trend.

Description

  • This function gives the Harmonic Mean of a given set of numbers.
  • Harmonic mean is used to calculate the average of a set of numbers.
  • The Harmonic mean is always the lowest mean.
  • Normally
  • Harmonic mean is defined as the reciprocal of the arithmetic mean by the reciprocals of a specified set of numbers.
  • The harmonic mean of a positive real numbers is defined by :

ie

.
  • In Parameters are any positive real numbers, and here First Parameter is required. From the second parameter are optional.
  • Also arguments can be numbers,names, arrays or references that contain numbers.
  • We can give logical values and text representations of numbers directly.
  • Suppose the arguments contains any text, logical values or empty cells like that values are ignored.
  • This will give the result as error when
1.The arguments with the error values or the referred text couldn't translated in to numbers.
2.Also any data .

ZOS

  • The syntax is to calculate HARMEAN in ZOS is .
    • Parameters are any set of positive real numbers.
  • For e.g.,HARMEAN(20..30,11..15,45.1..56.1..0.5)
Harmonic Mean

Examples

  1. =HARMEAN(1,2,3,4,5) = 2.18978102189781
  2. =HARMEAN(20,25,32,41) = 27.4649361523969
  3. =HARMEAN(0.25,5.4,3.7,10.1,15.2) = 1.0821913906985883
  4. =HARMEAN(3,5,0,2) = #N/A (NUMBER > 0 REQUIRED)
  5. =HARMEAN(1,-2,4) = #N/A (NUMBER > 0 REQUIRED)

Related Videos

Harmonic Mean

See Also

References

Harmonic mean


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