Difference between revisions of "Manuals/calci/HARMEAN"

Revision as of 02:59, 18 June 2014

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 $x_{1},x_{2},x_{3}....x_{n}>0$ is defined by :

$H={\frac {n}{(1/x_{1}+1/x_{2}+...+1/x_{n})}}$ 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  $point\leq 0$ .

The syntax is to calculate HARMEAN in ZOS is .
- $n1,n2,...$ are the positive real numbers.
For e.g.,HARMEAN(20..30,11..15,45.1..56.1..0.5)

=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

@@ Line 8: / Line 8: @@
 *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.
-*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>x_1,x_2,x_3....x_n > 0</math> is defined by :
-<math>H=\frac {n}{(1/x1+1/x2+...+1/xn)} </math>
+<math>H=\frac {n}{(1/x_1+1/x_2+...+1/x_n)} </math>
 ie
 :<math> H=\frac{n}{\sum_{i=1}^{n} \frac{1}{xi}}</math>.
@@ Line 39: / Line 39: @@
 ==References==
-[http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient Correlation]
+[http://en.wikipedia.org/wiki/Harmonic_mean Harmonic mean]