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 04:28, 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
- HARMEAN(1,2,3,4,5)=2.18978102189781
- HARMEAN(20,25,32,41)=27.4649361523969
- HARMEAN(0.25,5.4,3.7,10.1,15.2)=1.0821913906985883
- HARMEAN(3,5,0,2)=NAN
- HARMEAN(1,-2,4)=NAN
See Also