Difference between revisions of "Manuals/calci/HARMEAN"
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− | <div style="font-size:30px">'''HARMEAN( | + | <div style="font-size:30px">'''HARMEAN()'''</div><br/> |
− | * | + | *Parameters are any set of positive real numbers. |
+ | **HARMEAN(), returns values along an exponential trend. | ||
+ | |||
==Description== | ==Description== | ||
*This function gives the Harmonic Mean of a given set of numbers. | *This function gives the Harmonic Mean of a given set of numbers. | ||
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*Normally <math>Harmonic mean < Geometric mean < Arithmetic mean</math> | *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. | *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> | + | *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/ | + | <math>H=\frac {n}{(1/x_1+1/x_2+...+1/x_n)} </math> |
ie | ie | ||
:<math> H=\frac{n}{\sum_{i=1}^{n} \frac{1}{xi}}</math>. | :<math> H=\frac{n}{\sum_{i=1}^{n} \frac{1}{xi}}</math>. | ||
− | *In HARMEAN( | + | *In <math>HARMEAN(),</math> Parameters are any positive real numbers, and here First Parameter is required. From the second parameter 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. | ||
*We can give logical values and text representations of numbers directly. | *We can give logical values and text representations of numbers directly. | ||
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1.The arguments with the error values or the referred text couldn't translated in to numbers. | 1.The arguments with the error values or the referred text couldn't translated in to numbers. | ||
2.Also any data <math>point \le 0</math>. | 2.Also any data <math>point \le 0</math>. | ||
+ | |||
+ | ==ZOS== | ||
+ | *The syntax is to calculate HARMEAN in ZOS is <math>HARMEAN()</math>. | ||
+ | **Parameters are any set of 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}} | ||
==Examples== | ==Examples== | ||
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#=HARMEAN(20,25,32,41) = 27.4649361523969 | #=HARMEAN(20,25,32,41) = 27.4649361523969 | ||
#=HARMEAN(0.25,5.4,3.7,10.1,15.2) = 1.0821913906985883 | #=HARMEAN(0.25,5.4,3.7,10.1,15.2) = 1.0821913906985883 | ||
− | #=HARMEAN(3,5,0,2) = | + | #=HARMEAN(3,5,0,2) = #N/A (NUMBER > 0 REQUIRED) |
− | #=HARMEAN(1,-2,4) = | + | #=HARMEAN(1,-2,4) = #N/A (NUMBER > 0 REQUIRED) |
+ | |||
+ | ==Related Videos== | ||
+ | |||
+ | {{#ev:youtube|X3nQMiBK9rc|280|center|Harmonic Mean}} | ||
==See Also== | ==See Also== | ||
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*[[Manuals/calci/GEOMEAN | GEOMEAN ]] | *[[Manuals/calci/GEOMEAN | GEOMEAN ]] | ||
+ | ==References== | ||
+ | [http://en.wikipedia.org/wiki/Harmonic_mean Harmonic mean] | ||
− | + | ||
− | [ | + | |
+ | *[[Z_API_Functions | List of Main Z Functions]] | ||
+ | |||
+ | *[[ Z3 | Z3 home ]] |
Latest revision as of 05:03, 12 August 2020
HARMEAN()
- Parameters are any set of positive real numbers.
- HARMEAN(), returns values along an exponential trend.
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 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 :
ie
- .
- In Parameters are any positive real numbers, and here First Parameter is required. From the second parameter 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 .
ZOS
- The syntax is to calculate HARMEAN in ZOS is .
- Parameters are any set of positive real numbers.
- For e.g.,HARMEAN(20..30,11..15,45.1..56.1..0.5)
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) = #N/A (NUMBER > 0 REQUIRED)
- =HARMEAN(1,-2,4) = #N/A (NUMBER > 0 REQUIRED)
Related Videos
See Also
References