Manuals/calci/GEOMEAN

GEOMEAN(n1,n2,…)

• $n1,n2$ 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 and the geometric mean of the three numbers is the cube root of their product.
• So the geometric mean of n numbers is defined as the nth root of the product of the numbers.
• In GEOMEAN(n1,n2...)n1,n2.., are positive real numbers and n1 is required. 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 {a1,a2 ...,an} is given by:

[PI(){i=1 to n} ai] ^{1/n} = sqrt[n]{a1, a2 ... an}.

• This function will give the result as error when

1. Any one of the argument is nonnumeric
2. Any one value<=0
3. Any one of the references cannot be translated in to numbers.

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.

References

Gamma Distribution*