Difference between revisions of "Manuals/calci/HARMEAN"

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*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.
 
*The harmonic mean of a positive real numbers <math>x1,x2,x3....xn > 0</math> is defined by :
 
*The harmonic mean of a positive real numbers <math>x1,x2,x3....xn > 0</math> is defined by :
<math>H=\frac {n}{(1/x1+1/x2+...+1/xn)} = \frac{n}{\sum{i=1}^n \frac{1}{xi}}</math>.
+
<math>H=\frac {n}{(1/x1+1/x2+...+1/xn)} = \frac{n}{\sum{i=1}^{n} \frac{1}{xi}}</math>.
 
*In HARMEAN(n1,n2,...) n1,n2.. are the positive real numbers, and here n1 is required.n2,n3..., are optional.
 
*In HARMEAN(n1,n2,...) n1,n2.. are the positive real numbers, and here n1 is required.n2,n3..., 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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*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.
 
*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 point<=0.
 
2.Also any data point<=0.
 +
 
==Examples==
 
==Examples==
  

Revision as of 05:28, 10 December 2013

HARMEAN(n1,n2)


  • and are the positive real numbers.

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 < geometric mean < Arithmetic mean.
  • 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 :

.

  • In HARMEAN(n1,n2,...) n1,n2.. are the positive real numbers, and here n1 is required.n2,n3..., 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 point<=0.

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)=NAN
  5. HARMEAN(1,-2,4)=NAN

See Also


References

Correlation