Manuals/calci/HARMEAN

HARMEAN(n1,n2,...)

• $n1,n2,...$ 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(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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle point \le 0}
.

ZOS Section

• The syntax is to calculate HARMEAN in ZOS is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle HARMEAN(n1,n2,....)} .
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n1,n2,...} 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