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  2. Mean of a function - Wikipedia

    en.wikipedia.org/wiki/Mean_of_a_function

    In calculus, and especially multivariable calculus, the mean of a function is loosely defined as the average value of the function over its domain. In one variable, the mean of a function f ( x ) over the interval ( a , b ) is defined by: [ 1 ]

  3. Expected value - Wikipedia

    en.wikipedia.org/wiki/Expected_value

    In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average. Informally, the expected value is the mean of the possible values a random variable can take, weighted by the probability of those ...

  4. Mean - Wikipedia

    en.wikipedia.org/wiki/Mean

    In some circumstances, mathematicians may calculate a mean of an infinite (or even an uncountable) set of values. This can happen when calculating the mean value of a function (). Intuitively, a mean of a function can be thought of as calculating the area under a section of a curve, and then dividing by the length of that section.

  5. Mean value theorem - Wikipedia

    en.wikipedia.org/wiki/Mean_value_theorem

    The mean value theorem generalizes to real functions of multiple variables. The trick is to use parametrization to create a real function of one variable, and then apply the one-variable theorem. Let G {\displaystyle G} be an open subset of R n {\displaystyle \mathbb {R} ^{n}} , and let f : G → R {\displaystyle f:G\to \mathbb {R} } be a ...

  6. Logarithmic mean - Wikipedia

    en.wikipedia.org/wiki/Logarithmic_mean

    The area interpretation allows the easy derivation of some basic properties of the logarithmic mean. Since the exponential function is monotonic, the integral over an interval of length 1 is bounded by x and y. The homogeneity of the integral operator is transferred to the mean operator, that is (,) = (,).

  7. Average absolute deviation - Wikipedia

    en.wikipedia.org/wiki/Average_absolute_deviation

    The average absolute deviation (AAD) of a data set is the average of the absolute deviations from a central point. It is a summary statistic of statistical dispersion or variability. In the general form, the central point can be a mean , median , mode , or the result of any other measure of central tendency or any reference value related to the ...

  8. Root mean square - Wikipedia

    en.wikipedia.org/wiki/Root_mean_square

    So, the RMS value, I RMS, of the function I(t) is the constant current that yields the same power dissipation as the time-averaged power dissipation of the current I(t). Average power can also be found using the same method that in the case of a time-varying voltage, V(t), with RMS value V RMS,

  9. Root mean square deviation - Wikipedia

    en.wikipedia.org/wiki/Root_mean_square_deviation

    These deviations are called residuals when the calculations are performed over the data sample that was used for estimation (and are therefore always in reference to an estimate) and are called errors (or prediction errors) when computed out-of-sample (aka on the full set, referencing a true value rather than an estimate). The RMSD serves to ...