Difference between revisions of "Manuals/calci/HARMEAN"

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(Created page with "<div id="6SpaceContent" class="zcontent" align="left"> <font size="3"><font face="Times New Roman">'''HARMEAN''' (N'''1''', N2...)</font></font> <font size="3"><font fac...")
 
 
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<div style="font-size:30px">'''HARMEAN()'''</div><br/>
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*Parameters are any set of positive real numbers.
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**HARMEAN(), returns values along an exponential trend.
  
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<font size="3"><font face="Times New Roman">'''HARMEAN''' (N'''1''', N2...)</font></font>
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==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 <math>Harmonic mean < Geometric mean < Arithmetic mean</math>
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*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 <math>x_1,x_2,x_3....x_n > 0</math> is defined by :
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<math>H=\frac {n}{(1/x_1+1/x_2+...+1/x_n)} </math>
 +
ie
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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.
 +
*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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*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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<font size="3"><font face="Times New Roman">'''Where N1, N2 ...'''   n1, n2 etc are parameters. You can also give as an array or use array reference.</font></font>
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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.
 +
*For e.g.,HARMEAN(20..30,11..15,45.1..56.1..0.5)
 +
{{#ev:youtube|oHiCLVUJz-4|280|center|Harmonic Mean}}
  
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</div>
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==Examples==
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<div id="1SpaceContent" class="zcontent" align="left">
 
  
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<font size="3"><font face="Times New Roman">Calci returns the harmonic mean of a data set. It is the reciprocal of the arithmetic mean of reciprocals. </font></font>
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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(0.25,5.4,3.7,10.1,15.2) = 1.0821913906985883                 
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#=HARMEAN(3,5,0,2) = #N/A (NUMBER > 0 REQUIRED)
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#=HARMEAN(1,-2,4) = #N/A (NUMBER > 0 REQUIRED)
  
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</div>
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==Related Videos==
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<div id="7SpaceContent" class="zcontent" align="left">
 
  
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<font size="3">·</font>        <font size="3"><font face="Times New Roman">HM &lt;GM&lt;AM. </font></font>
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{{#ev:youtube|X3nQMiBK9rc|280|center|Harmonic Mean}}
  
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<font size="3">·</font>        <font size="3"><font face="Times New Roman">The values are ignored, when an array or reference argument contains text, logical values, or empty cells. </font></font>
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==See Also==
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*[[Manuals/calci/AVERAGE  | AVERAGE ]]
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*[[Manuals/calci/GEOMEAN  | GEOMEAN ]]
  
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<font size="3">·</font>        <font size="3"><font face="Times New Roman">Logical values and text representations of numbers are counted. </font></font>
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==References==
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[http://en.wikipedia.org/wiki/Harmonic_mean Harmonic mean]
  
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<font size="3">·</font>        <font size="3"><font face="Times New Roman">HARMEAN calculates an error value, when any data point ≤ 0. </font></font>
 
  
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<font size="3"><font face="Times New Roman"></font></font>
 
  
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<font size="3"><font face="Times New Roman">
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*[[Z_API_Functions | List of Main Z Functions]]
  
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Formulas:-
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*[[ Z3 |  Z3 home ]]
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<font size="3"><font face="Times New Roman">To find out the harmonic mean, the equation is: </font></font>
 
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</font></font></div>
 
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<div id="12SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="left">
 
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HARMEAN
 
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</div></div>
 
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<div id="8SpaceContent" class="zcontent" align="left">
 
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Lets see an example in (Column1, Row1)
 
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<nowiki>=HARMEAN (B1:B6) That is </nowiki>
 
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<nowiki>=HARMEAN(5,6,7,9,12,13) is 7.68</nowiki>
 
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</div>
 
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<div id="10SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Syntax </div><div class="ZEditBox"><center></center></div></div>
 
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<div id="4SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Remarks </div></div>
 
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<div id="3SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Examples </div></div>
 
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<div id="11SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Description </div></div>
 
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| class="sshl_f" | 7.683527
 
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<div align="left">[[Image:calci1.gif]]</div></div>
 
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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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