Difference between revisions of "Manuals/calci/HARMEAN"

Revision as of 13:30, 8 May 2015

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(n_1,n_2,...) $n_{1},n_{2}..$ are the positive real numbers, and here $n_{1}$ is required. $n_{2},n_{3}...$ , 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 .
- $n_{1},n_{2},...$ are the positive real numbers.
For e.g.,HARMEAN(20..30,11..15,45.1..56.1..0.5)

Harmonic Mean

=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) = #ERROR
=HARMEAN(1,-2,4) = #ERROR

@@ Line 1: / Line 1: @@
 <div style="font-size:30px">'''HARMEAN(n1,n2,...)'''</div><br/>
-*<math>n1,n2,...</math> are the positive real numbers.
+*<math>n_1,n_2,...</math> are the positive real numbers.
 ==Description==
@@ Line 12: / Line 12: @@
 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(n_1,n_2,...) <math>n_1,n_2..</math> are the positive real numbers, and here <math>n_1</math> is required. <math>n_2,n_3...</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.
@@ Line 21: / Line 21: @@
 ==ZOS Section==
-*The syntax is to calculate HARMEAN in ZOS is <math>HARMEAN(n1,n2,....)</math>.
+*The syntax is to calculate HARMEAN in ZOS is <math>HARMEAN(n_1,n_2,....)</math>.
-**<math>n1,n2,...</math> are the positive real numbers.
+**<math>n_1,n_2,...</math> are the 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}}