Difference between revisions of "Manuals/calci/GEOMEAN"
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| − | <div | + | <div style="font-size:30px">'''GEOMEAN()'''</div><br/> |
| + | *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 <math>n</math> numbers is defined as the <math>n^{th}</math> root of the product of the numbers. | ||
| + | *In <math>GEOMEAN()</math>, 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 <math>[a_1,a_2,...a_n]</math> is given by: | ||
| + | <math>({\prod_{i=1}^n a_i})^{\frac{1}{n}} = \sqrt[n]{a_1, a_2 ... a_n}</math> | ||
| + | *This function will give the result as error when | ||
| + | 1.Any one of the argument is non-numeric | ||
| + | 2.Any one <math>value \le 0</math> | ||
| + | 3.Any one of the references cannot be translated in to numbers. | ||
| − | < | + | ==ZOS== |
| + | *The syntax is to calculate GEOMEAN in ZOS is <math>GEOMEAN()</math>. | ||
| + | **Parameters are any set of positive real numbers. | ||
| + | *For e.g.,GEOMEAN(1,2,3,4,5),GEOMEAN(11.5..20.5..0.5) | ||
| + | {{#ev:youtube|me2sEpY6LD4|280|center|Geometric Mean}} | ||
| − | + | ==Examples== | |
| − | + | #=GEOMEAN(3,27) = 9 | |
| − | + | #=GEOMEAN(2,4,8) = 3.9999999999999996 | |
| + | #=GEOMEAN(3,5,8,10,12) = 6.786916380543178 | ||
| + | #=GEOMEAN(-2,32) = #N/A (NUMBER > 0 REQUIRED) | ||
| − | + | ==Related Videos== | |
| − | + | {{#ev:youtube|s-DXD1W48A8|280|center|Geometric Mean}} | |
| − | - | ||
| − | |||
| − | + | ==See Also== | |
| + | *[[Manuals/calci/AVERAGE | AVERAGE ]] | ||
| + | *[[Manuals/calci/SUM | SUM ]] | ||
| + | *[[Manuals/calci/TRIMMEAN |TRIMMEAN ]] | ||
| − | + | ==References== | |
| + | *[http://en.wikipedia.org/wiki/Geometric_mean| Geometric Mean] | ||
| − | |||
| − | |||
| − | + | *[[Z_API_Functions | List of Main Z Functions]] | |
| − | [[ | + | *[[ Z3 | Z3 home ]] |
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Latest revision as of 04:01, 12 August 2020
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 numbers is defined as the root of the product of the numbers.
- In , 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 is given by:
numbers is defined as the 
root of the product of the numbers.
, Parameters are any set of positive real numbers and first parameter is required. From second parameters are optional.![{\displaystyle [a_{1},a_{2},...a_{n}]}](https://wikimedia.org/api/rest_v1/media/math/render/png/5e533f241c5458f6100761fe356b6ca23183bd07)
is given by:
![{\displaystyle ({\prod _{i=1}^{n}a_{i}})^{\frac {1}{n}}={\sqrt[{n}]{a_{1},a_{2}...a_{n}}}}](https://wikimedia.org/api/rest_v1/media/math/render/png/64b3a770085f0974320a2ea02fbcb0e8a344cab7)
- This function will give the result as error when
1.Any one of the argument is non-numeric 2.Any one 3.Any one of the references cannot be translated in to numbers.
3.Any one of the references cannot be translated in to numbers.
ZOS
- The syntax is to calculate GEOMEAN in ZOS is .
- Parameters are any set of positive real numbers.
- For e.g.,GEOMEAN(1,2,3,4,5),GEOMEAN(11.5..20.5..0.5)
Examples
- =GEOMEAN(3,27) = 9
- =GEOMEAN(2,4,8) = 3.9999999999999996
- =GEOMEAN(3,5,8,10,12) = 6.786916380543178
- =GEOMEAN(-2,32) = #N/A (NUMBER > 0 REQUIRED)
Related Videos
See Also
References