Manuals/calci/HARMEAN

HARMEAN(n1,n2,...)

• $n_{1},n_{2},...$ 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 $Harmonicmean<Geometricmean<Arithmeticmean$
• 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 $point\leq 0$.

ZOS

• The syntax is to calculate HARMEAN in ZOS is $HARMEAN(n_{1},n_{2},....)$.
  • $n_{1},n_{2},...$ are the positive real numbers.
• For e.g.,HARMEAN(20..30,11..15,45.1..56.1..0.5)

Harmonic Mean

Examples

1. =HARMEAN(1,2,3,4,5) = 2.18978102189781
2. =HARMEAN(20,25,32,41) = 27.4649361523969
3. =HARMEAN(0.25,5.4,3.7,10.1,15.2) = 1.0821913906985883
4. =HARMEAN(3,5,0,2) = #ERROR
5. =HARMEAN(1,-2,4) = #ERROR

See Also

• AVERAGE
• GEOMEAN

References

Harmonic mean