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IEVref: | 103-02-04 | ID: | |

Language: | en | Status: Standard | |

Term: | geometric mean value | ||

Synonym1: | geometric average [Preferred] | ||

Synonym2: | |||

Synonym3: | |||

Symbol: | |||

Definition: | quantity representing the quantities in a finite set or in an interval,- for
*n*positive quantities ${x}_{1},\text{\hspace{0.17em}}{x}_{2},\text{\hspace{0.17em}}\text{\hspace{0.17em}}\dots \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{x}_{n}$, by the positive*n*th root of their product:$X}_{\text{g}}={({x}_{1}\cdot {x}_{2}\cdot \mathrm{...}\cdot {x}_{n})}^{1/n$ - for a quantity
*x*depending on a variable*t*, by the quantity ${X}_{\text{g}}$ calculated from the values of the quantity*x*(*t*) by the expression$\mathrm{log}\frac{{X}_{\text{g}}}{{x}_{\text{ref}}}=\frac{1}{T}{\int}_{\text{\hspace{0.05em}}0}^{\text{\hspace{0.05em}}T}\mathrm{log}\frac{x(t)}{{x}_{\text{ref}}}\text{d}t$ where ${x}_{\text{ref}}$ is a reference value
Note 1 to entry: The geometric mean value of a periodic quantity is usually taken over an integration interval the range of which is the period multiplied by a natural number. Note 2 to entry: The geometric mean value of a quantity is denoted by adding the subscript g to the symbol of the quantity. | ||

Publication date: | 2017-07 | ||

Source: | |||

Replaces: | 103-02-04:2009:12 | ||

Internal notes: | 2017-08-25: Added <p> tag before list. LMO | ||

CO remarks: | |||

TC/SC remarks: | |||

VT remarks: | |||

Domain1: | |||

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Domain5: |

- for
*n*positive quantities ${x}_{1},\text{\hspace{0.17em}}{x}_{2},\text{\hspace{0.17em}}\text{\hspace{0.17em}}\dots \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{x}_{n}$, by the positive*n*th root of their product:$X}_{\text{g}}={({x}_{1}\cdot {x}_{2}\cdot \mathrm{...}\cdot {x}_{n})}^{1/n$

- for a quantity
*x*depending on a variable*t*, by the quantity ${X}_{\text{g}}$ calculated from the values of the quantity*x*(*t*) by the expression$\mathrm{log}\frac{{X}_{\text{g}}}{{x}_{\text{ref}}}=\frac{1}{T}{\int}_{\text{\hspace{0.05em}}0}^{\text{\hspace{0.05em}}T}\mathrm{log}\frac{x(t)}{{x}_{\text{ref}}}\text{d}t$

where ${x}_{\text{ref}}$ is a reference value

Note 1 to entry: The geometric mean value of a periodic quantity is usually taken over an integration interval the range of which is the period multiplied by a natural number.

Note 2 to entry: The geometric mean value of a quantity is denoted by adding the subscript g to the symbol of the quantity.