Manuals/calci/HARMEAN

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.

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 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 Harmonic mean < Geometric mean < Arithmetic mean}
• 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 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 x_1,x_2,x_3....x_n > 0} is defined by :

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 H=\frac {n}{(1/x_1+1/x_2+...+1/x_n)} } ie

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 H=\frac{n}{\sum_{i=1}^{n} \frac{1}{xi}}} .

• In 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, and here 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} is required. 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 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 $point\leq 0$.

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