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.
• 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 $n^{th}$ root of the product of the numbers.
• In $GEOMEAN(n1,n2...)$, $n1,n2...$ are the 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:

$({\prod _{i=1}^{n}ai})^{\frac {1}{n}}={\sqrt[{n}]{a1,a2...an}}$

• This function will give the result as error when

1.Any one of the argument is non-numeric
2.Any one $value\leq 0$
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*