Manuals/calci/GEOMEAN

GEOMEAN(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 Geometric Mean of an array or references.
• For example, it is used to calculate average rate of growth of human population.
• The Geometric Mean of two numbers is, the square root of their product.
• The Geometric Mean of the three numbers is, the cube root of their product.
• So the geometric mean of 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 n} numbers is defined as the 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 n^{th}} root of the product of the numbers.
• In 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 GEOMEAN(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 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.
• The arguments can be numbers,names,arrays or references that contain numbers.
• Also we can directly use logical values and text representations of numbers.
• The values are ignored, when the argument contains logical values or empty cells.
• The Geometric and Arithmetic Means are equal, when all the numbers in the given set are equal, otherwise the Geometric Mean of a data set is less than the data set's Arithmetic Mean.
• The geometric mean of a data set 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 [a_1,a_2,...a_n]} is given 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 ({\prod_{i=1}^n a_i})^{\frac{1}{n}} = \sqrt[n]{a_1, a_2 ... a_n}}

• This function will give the result as error when

1.Any one of the argument is non-numeric
2.Any one 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 value \le 0}

3.Any one of the references cannot be translated in to numbers.

ZOS Section

• The syntax is to calculate GEOMEAN 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 GEOMEAN(n1,n2,...)} .
  • $n1,n2...$ are the positive real numbers.
• For e.g.,geomean(1,2,3,4,5),geomean(11.5..20.5..0.5)

Examples

1. =GEOMEAN(3,27) = 9
2. =GEOMEAN(2,4,8) = 4
3. =GEOMEAN(3,5,8,10,12) = 6.786916380543178
4. =GEOMEAN(-2,32) = NAN, because the value is < 0.

See Also

• AVERAGE
• SUM
• MEAN

References

• Geometric Mean