Manuals/calci/GEOMEAN

GEOMEAN()

• Parameters are any set of positive real numbers.
  • GEOMEAN(),Returns the geometric mean.

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 $GEOMEAN()$, Parameters are any set of positive real numbers and first parameter is required. From second parameters 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 $[a_{1},a_{2},...a_{n}]$ is given by:

$({\prod _{i=1}^{n}a_{i}})^{\frac {1}{n}}={\sqrt[{n}]{a_{1},a_{2}...a_{n}}}$

• This function will give the result as error when

1.Any one of the argument is non-numeric
2.Any one $value\leq 0$
3.Any one of the references cannot be translated in to numbers.

ZOS

• The syntax is to calculate GEOMEAN in ZOS is $GEOMEAN()$.
  • Parameters are any set of positive real numbers.
• For e.g.,GEOMEAN(1,2,3,4,5),GEOMEAN(11.5..20.5..0.5)

Geometric Mean

Examples

1. =GEOMEAN(3,27) = 9
2. =GEOMEAN(2,4,8) = 3.9999999999999996
3. =GEOMEAN(3,5,8,10,12) = 6.786916380543178
4. =GEOMEAN(-2,32) = #ERROR, because the value is < 0.

Related Videos

Geometric Mean

See Also

• AVERAGE
• SUM
• TRIMMEAN

References

• Geometric Mean

• List of Main Z Functions

• Z3 home