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IEVref: | 103-02-05 | ID: | |

Language: | en | Status: Standard | |

Term: | harmonic mean value | ||

Synonym1: | harmonic average [Preferred] | ||

Synonym2: | |||

Synonym3: | |||

Symbol: | |||

Definition: | quantity representing the quantities in a finite set or in an interval,- for
*n*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 reciprocal of the mean value of their reciprocals:$\frac{1}{{X}_{\text{h}}}=\frac{1}{n}\left(\frac{1}{{x}_{1}}+\frac{1}{{x}_{2}}+\mathrm{...}+\frac{1}{{x}_{n}}\right)$ if none of the *n*quantities is equal to zero;${X}_{\text{h}}=0$ if at least one quantity is equal to zero; - for a quantity
*x*depending on a variable*t*, by the quantity ${X}_{\text{h}}$ defined by the reciprocal of the mean value of the reciprocal of the given quantity:$\frac{1}{{X}_{\text{h}}}=\frac{1}{T}{\int}_{\text{\hspace{0.05em}}0}^{\text{\hspace{0.05em}}T}\frac{1}{x(t)}\text{d}t$ if the value of the integral is finite; ${X}_{\text{h}}=0$ in other cases
Note 1 to entry: The harmonic 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 harmonic mean value of a quantity is denoted by adding the subscript h to the symbol of the quantity. | ||

Publication date: | 2017-07 | ||

Source: | |||

Replaces: | 103-02-05:2009-12 | ||

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

CO remarks: | |||

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- for
*n*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 reciprocal of the mean value of their reciprocals:$\frac{1}{{X}_{\text{h}}}=\frac{1}{n}\left(\frac{1}{{x}_{1}}+\frac{1}{{x}_{2}}+\mathrm{...}+\frac{1}{{x}_{n}}\right)$ if none of the

*n*quantities is equal to zero;${X}_{\text{h}}=0$ if at least one quantity is equal to zero;

- for a quantity
*x*depending on a variable*t*, by the quantity ${X}_{\text{h}}$ defined by the reciprocal of the mean value of the reciprocal of the given quantity:$\frac{1}{{X}_{\text{h}}}=\frac{1}{T}{\int}_{\text{\hspace{0.05em}}0}^{\text{\hspace{0.05em}}T}\frac{1}{x(t)}\text{d}t$ if the value of the integral is finite;

${X}_{\text{h}}=0$ in other cases

Note 1 to entry: The harmonic 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 harmonic mean value of a quantity is denoted by adding the subscript h to the symbol of the quantity.