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IEVref: | 103-02-01 | ID: | |

Language: | en | Status: Standard | |

Term: | mean value | ||

Synonym1: | mean [Preferred] | ||

Synonym2: | arithmetic mean [Preferred] | ||

Synonym3: | average<br>arithmetic average [Preferred] | ||

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 quotient of the sum of the quantities by*n*:$\overline{X}={\displaystyle \frac{1}{n}({x}_{1}+{x}_{2}+\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\dots \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}+{x}_{n})}$ - for a quantity
*x*depending on a variable*t*, by the integral of the quantity taken between two given values of the variable, divided by the difference of the two values:$\overline{X}=\frac{1}{{t}_{2}-{t}_{1}}{\displaystyle {\int}_{\text{\hspace{0.05em}}{t}_{1}}^{\text{\hspace{0.05em}}{t}_{2}}x(t)\text{d}t}$
Note 1 to entry: The 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 mean value of the quantity Note 3 to entry: The adjective "arithmetic" is only used to qualify the terms "mean" and "average" in order to distinguish them from the terms "geometric mean" and "geometric average", as well from "harmonic mean" and "harmonic average". Note 4 to entry: The mean value can be generalized for a function of | ||

Publication date: | 2017-07 | ||

Source: | |||

Replaces: | 103-02-01:2009-12 | ||

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

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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 quotient of the sum of the quantities by*n*:$\overline{X}={\displaystyle \frac{1}{n}({x}_{1}+{x}_{2}+\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\dots \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}+{x}_{n})}$

- for a quantity
*x*depending on a variable*t*, by the integral of the quantity taken between two given values of the variable, divided by the difference of the two values:$\overline{X}=\frac{1}{{t}_{2}-{t}_{1}}{\displaystyle {\int}_{\text{\hspace{0.05em}}{t}_{1}}^{\text{\hspace{0.05em}}{t}_{2}}x(t)\text{d}t}$

Note 1 to entry: The 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 mean value of the quantity *x* may be denoted by $\overline{X}$, by ⟨*X*⟩, or by *X*_{a}. Subscripts ar, av and moy are also used.

Note 3 to entry: The adjective "arithmetic" is only used to qualify the terms "mean" and "average" in order to distinguish them from the terms "geometric mean" and "geometric average", as well from "harmonic mean" and "harmonic average".

Note 4 to entry: The mean value can be generalized for a function of *n* variables, e.g. with a surface integral or an integral over a three-dimensional domain divided by the corresponding area or volume. See the examples in IEC 60050-102.