Difference between revisions of "Manuals/calci/HARMEAN"

Revision as of 05:44, 10 December 2013

HARMEAN(n1,n2)

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 $Harmonicmean<geometricmean<Arithmeticmean$
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 $x1,x2,x3....xn>0$ is defined by :

$H={\frac {n}{(1/x1+1/x2+...+1/xn)}}$ ie

H={\frac {n}{\sum _{i=1}^{n}{\frac {1}{xi}}}}

.

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  $point\leq 0$ .

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

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 ie
 :<math> H=\frac{n}{\sum_{i=1}^{n} \frac{1}{xi}}</math>.
-*In HARMEAN(n1,n2,...) <math>n1,n2..</math> are the positive real numbers, and here </math>n1</math> is required.< <math>n2,n3...</math>, are optional.
+*In HARMEAN(n1,n2,...) <math>n1,n2..</math> are the positive real numbers, and here <math>n1</math> is required.< <math>n2,n3...</math>, 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.