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        Word: cnanfadi [jbovlaste]
        Type: fu'ivla
  Gloss Word: arithmetic mean
  Gloss Word: average in the sense of "generalized f-mean"
  Gloss Word: generalized f-mean
  Gloss Word: generalized mean
  Gloss Word: geometric mean
  Gloss Word: harmonic mean
  Gloss Word: log-sum-exponential
  Gloss Word: LSE in the sense of "log-sum-exponential"
  Gloss Word: max
  Gloss Word: mean in the sense of "generalized f-mean"
  Gloss Word: mean value
  Gloss Word: min
  Gloss Word: norm in the sense of "average, typical, or 'normal' value"
  Gloss Word: norm in the sense of "math terminology, specifically p-norm"
  Gloss Word: p-norm
  Gloss Word: power mean
  Gloss Word: quasi-arithmetic mean
  Gloss Word: RMS in the sense of "root-mean-square"
  Gloss Word: root-mean-square
  Gloss Word: typical in the sense of "average value"
  Definition: x1 (li; number/quantity) is the weighted quasi-arithmetic
       mean/generalized f-mean of/on data x2 (completely specified
       ordered multiset/list) using function x3 (defaults according to
       the notes; if it is an extended-real number, then it has a
       particular interpretation according to the Notes) with weights
       x4 (completely specified ordered multiset/list with same
       cardinality/length as x2; defaults according to Notes).
       Notes: Potentially dimensionful. Make sure to convert x3 from an
       operator to a sumti; x3 is the 'f' in "f-mean" and must be a
       complex-valued, single-valued function which is defined and
       continuous on x2 and which is injective; it defaults to the
       $p$th-power function ($z^p$) for some nonzero $p$ (note that it
       need not be positive or an integer) and
       indeterminate/variable/input $z$, or $log$, or $exp$ (as
       functions); culture or context can further constrain the
       default. If x2 is set to "$z^+ \infty .$" (the exponent is
       positive infinity, given by "ma'uci'i") for
       indeterminate/variable $z$ (the function is the functional
       limit of the monic, single-term polynomial as the degree
       increases without bound), then the result (x1) is the
       weight-sum-scaled maximum of the products of the data (terms of
       x2) with their corresponding weights (terms of x4) according to
       the standard ordering on the set of all real numbers or
       possibly some other specified or assumed ordering; likewise, if
       x2 is set to "$z^- \infty .$" (the exponent is negative
       infinity, given by "ni'uci'i") for indeterminate/variable $z$
       (the function is the functional limit of the monic, single-term
       reciprocal-polynomial as the reciprocal-degree increases
       without bound (or the degree decreases without bound)), then
       the result (x1) is the weight-sum-scaled minimum of the
       products of the data (terms of x2) with their corresponding
       weights (terms of x4) according to the standard ordering on the
       set of all real numbers or possibly some other specified or
       assumed ordering. The default of x4 is the ordered set of $n$
       terms with each term equal identically to $1/n$, where the
       cardinality of x2 is $n$. Let "$f$" denote the sumti in x3,
       "$y_i$" denote the $i$th term in x2 for all $i$, "$n$" denote
       the cardinality of x2 (thus also x4), and "$w_i$" denote the
       $i$th term in x4 for any $i$; then the result x1 is equal to:
       $f^(-1)($Sum$(w_i f(y_i), i$ in Set$(1,...,n)) / $Sum$(w_i,
       i$ in Set$(1,...,n)))$. Note that if the weights are all $1$
       and x2 is set equal to not the $p$th-power function, but
       instead the $p$th-power function left-composed with the
       absolute value function (or the forward difference function),
       then the result is the $p$-norm on x2 scaled by $n^(-1/p)$
       for integer $n$ being the cardinality of x2. This should
       typically not refer to the mean of a function (
       https://en.wikipedia.org/wiki/Mean_of_a_function ), although it
       generalizes easily; alternatively, with appropriate weighting,
       allow x2 to be the image (set) of the function whose average is
       desired over the entire relevant subset of its domain - notice
       that the weights will have to themselves be functions of the
       data or the domain of the function; in this context, the
       function is not necessarily x3. If x3 is a single extended-real
       number $p$ (not a function), then this word refers to the
       weighted power-mean and it is equivalent to letting x2 equal
       the $p$th-power function as before iff $p$ is nonzero real, the
       $max$ or $min$ as before if $p$ is infinite (according to its
       signum as before), and $log$ if $p=0$ (thus making the overall
       mean refer to the geometric mean); this overloading is for
       convenience of usage and will not cause confusion because
       constant functions are very much so not injective.