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Anonymous shared the following library of statistical functions with us. Many thanks! (He added, that they are not checked...)

fricas
)abbrev package STAT StatPackage
++ Description:
++ This package exports statistic utilities
StatPackage(S,A) : Exports == Implementation where 
  S: SetCategory
  A: Join(Collection(S), finiteAggregate)
  Exports == with
        if A has FiniteLinearAggregate(S) and S has OrderedSet then
                median: A -> S
                ++ median(a) median of a collection (ordering from OrderedSet)
        if S has Field then
                mean: A -> S
                ++ mean(a) arithmetic mean of a collection
                hmean: A -> S
                ++ hmean(a) harmonic mean of a collection
                moment: (A,Integer) -> S
                ++ moment(a,i) i nth moment of a collection
                variance: A -> S
                ++ variance(a) variance of a collection
                center: A -> A
                ++ center(a) center collection
                if A has shallowlyMutable then
                        center!: A -> A
                        ++ center!(a) center collection
                if S has RadicalCategory then
                        gmean: A -> S
                        ++ gmean(a) geometric mean of a collection
                        stdev: A -> S
                        ++ stdev(a) root mean square of a collection
                        stdize: A -> A
                        ++ stdize(a) standardize a collection   
                        if A has shallowlyMutable then
                                stdize!: A -> A
                                ++ stdize!(a) standardize a collection  
  Implementation == add
if A has FiniteLinearAggregate(S) and S has OrderedSet then median(m)== n := sort(m) i:= divide(#m,2) if (zero? i.remainder) then j:= elt(n,i.quotient+minIndex(m)-1) else j:= elt(n,i.quotient+minIndex(m)) j
if S has Field then if A has OneDimensionalArrayAggregate(S) then sums: A ->List S sums(m)== j:=0::S j2:=0::S for i in minIndex(m)..maxIndex(m) repeat h:= elt(m,i) j := j + h j2 := j2 + h*h [j,j2] variance(m)== i := center(m) s := sums(i) k := (s.2 - s.1/#m::S)/(#m::S - 1::S) k if S has RadicalCategory then stdize(m)== i := mean(m) j := map(xx +-> xx-i, m) s := sums(j) k := sqrt((s.2 - s.1/#m::S)/(#m::S - 1::S)) map(xx +-> (xx-i)/k,m) if A has shallowlyMutable then stdize!(m)== i := mean(m) j := map(xx +-> xx - i, m) s := sums(j) k := sqrt((s.2 - s.1/#m::S)/(#m::S - 1::S)) map!(xx +-> (xx - i)/k, m)
else variance(m)== i := center(m) j := reduce("+",i) j2 := reduce("+", map(xx +-> xx*xx,i)) k := (j2 - j/#m::S)/(#m::S - 1::S) k if S has RadicalCategory then stdize(m)== me:= mean(m) i := map(xx +-> xx - me, m) j := reduce("+",i) j2 := reduce("+", map(xx +-> xx*xx,i)) k := sqrt((j2 - j/#m::S)/(#m::S - 1::S)) map(xx +-> (xx -me)/k,m) if A has shallowlyMutable then stdize!(m)== me:= mean(m) i := map(xx +-> xx - me,m) j := reduce("+",i) j2 := reduce("+", map(xx +-> xx*xx, i)) k := sqrt((j2 - j/#m::S)/(#m::S - 1::S)) map!(xx +->(xx - me)/k, m)
if A has FiniteLinearAggregate(S) and S has OrderedSet then median(m)== n := sort(m) min := minIndex(m) i:= divide(#m,2) if (zero? i.remainder) then j:= (elt(n,i.quotient+min-1)+elt(n,i.quotient+min))/2::S else j:=elt(n,i.quotient+min) j mean(m)== i := reduce("+", m) (i / (#m::S))
hmean(m)== i := map(xx +-> 1::S/xx, m) j := reduce("+", i) ((#m::S) / j)
moment(m,n)== n = 0 => 1 n = 1 => mean(m) i := map(xx +-> xx^n, m) j := reduce("+",i) (j / (#m::S))
center(m)== i := mean(m) map(xx +-> xx - i, m)
if A has shallowlyMutable then center!(m)== i := mean(m) map!(xx +-> xx - i, m) m if S has RadicalCategory then gmean(m)== i := reduce("*", m) nthRoot(i,#m)
stdev(m)== sqrt(variance(m))
fricas
)abbrev package IDSTAT IntegralDomainStatPackage
++ Description:
++ This package exports statistic utilities over IntegralDomain
IntegralDomainStatPackage(S,A) : Exports == Implementation where 
  S: IntegralDomain
  A: Join(Collection(S), finiteAggregate)
  Exports == with
        mean: A -> Fraction(S)
        ++ mean(a) arithmetic mean of a collection
        moment: (A,NonNegativeInteger) -> Fraction(S)
        ++ moment(m,n) nth moment of a collection
Implementation == add mean(m)== i := reduce("+", m) i / #m::S moment(m,n)== n = 0 => 1 n = 1 => mean(m) i := map(xx +-> xx^n, m) j := reduce("+",i) j / #m::S
fricas
)abbrev package MSTAT MatrixStatPackage
++ Description:
++ This package exports statistic utilities on two dimensional arrays
++ Function are applied column by column
MatrixStatPackage(S,Row,Col,M) : Exports == Implementation where 
  S: SetCategory
  Row : FiniteLinearAggregate S
  Col : FiniteLinearAggregate S
  M   : TwoDimensionalArrayCategory(S,Row,Col)
  Exports == with
        if Col has shallowlyMutable then
                if S has OrderedSet then
                        median: M -> Col
                        ++ median(a) median of a two dimensional array (ordering from OrderedSet)
                if S has Field then
                        mean: M -> Col
                        ++ mean(a) arithmetic mean of a two dimensional array
                        hmean: M -> Col
                        ++ hmean(a) harmonic mean of a two dimensional array
                        variance: M -> Col
                        ++ variance(a) variance of a two dimensional array
                        moment: (M,Integer) -> Col
                        ++ moment(a,i) i nth moment of a two dimensional array
                        center: M -> M
                        ++ center(a) center two dimensional array
                        center!: M -> M
                        ++ center!(a) center two dimensional array
                        if M has MatrixCategory(S,Row,Col) then
                                cov:  M -> M
                                ++ cov(a): covariance matrix
                        if S has RadicalCategory then
                                gmean: M -> Col
                                ++ gmean(a) geometric mean of a two dimensional array
                                stdev: M -> Col
                                ++ stdev(a) root mean square of a two dimensional array
                                stdize: M -> M
                                ++ stdize(a) standardize two dimensional array
                                stdize!: M -> M
                                ++ stdize!(a) standardize two dimensional array
                                if M has MatrixCategory(S,Row,Col) then
                                        cor:  M -> M
                                        ++ cor(a): correlation matrix
Implementation == add import StatPackage(S,Col) if Col has shallowlyMutable then colReduce: (Col -> S, M) -> Col colReduce(fx,m)== ret : Col := new(ncols(m),NIL$Lisp) j := minColIndex(m) - 1 for i in j+1..maxColIndex(m) repeat setelt!(ret,i-j,fx(column(m,i))) ret if S has OrderedSet then median(m) == ret := colReduce(median$StatPackage(S,Col),m) ret if S has Field then mean(m)== ret := colReduce(mean$StatPackage(S,Col),m) ret hmean(m)== ret := colReduce(hmean$StatPackage(S,Col),m) ret variance(m)== ret := colReduce(variance$StatPackage(S,Col),m) ret moment(m,pow)== ret : Col := new(ncols(m),NIL$Lisp) j := minColIndex(m) - 1 for i in j+1..maxColIndex(m) repeat setelt!(ret,i,moment(column(m,i),pow)$StatPackage(S,Col)) ret center(m)== ret : M := new(nrows(m),ncols(m),NIL$Lisp) j := minColIndex(m) - 1 for i in j+1..maxColIndex(m) repeat setColumn!(ret,i-j,center!(column(m,i))$StatPackage(S,Col)) ret center!(m)== j := minColIndex(m) - 1 for i in j+1..maxColIndex(m) repeat setColumn!(m,i-j,center!(column(m,i))$StatPackage(S,Col)) m if M has MatrixCategory(S,Row,Col) then cov(m)== ret := center(m) transpose(ret/(nrows(m)-1)::S) * ret
if S has RadicalCategory then gmean(m)== colReduce(gmean$StatPackage(S,Col),m) stdev(m)== colReduce(stdev$StatPackage(S,Col),m) stdize(m)== ret : M := new(nrows(m),ncols(m),NIL$Lisp) j := minColIndex(m) - 1 for i in j+1..maxColIndex(m) repeat setColumn!(ret,i-j,stdize!(column(m,i))$StatPackage(S,Col)) ret stdize!(m)== j := minColIndex(m) - 1 for i in j+1..maxColIndex(m) repeat setColumn!(m,i-j,stdize!(column(m,i))$StatPackage(S,Col)) m if M has MatrixCategory(S,Row,Col) then cor(m)== ret := stdize(m) (transpose(ret/((nrows(m)-1)::S)) * ret)
fricas
Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/172717192283825040-25px.001.spad
      using old system compiler.
   STAT abbreviates package StatPackage 
------------------------------------------------------------------------
   initializing NRLIB STAT for StatPackage 
   compiling into NRLIB STAT 
****** Domain: A already in scope
****** Domain: A already in scope
augmenting A: (FiniteLinearAggregate S)
****** Domain: S already in scope
augmenting S: (OrderedSet)
augmenting $: (SIGNATURE $ median (S A))
   compiling exported median : A -> S
Time: 0.03 SEC.
****** Domain: S already in scope augmenting S: (Field) augmenting $: (SIGNATURE $ mean (S A)) augmenting $: (SIGNATURE $ hmean (S A)) augmenting $: (SIGNATURE $ moment (S A (Integer))) augmenting $: (SIGNATURE $ variance (S A)) augmenting $: (SIGNATURE $ center (A A)) ****** Domain: A already in scope augmenting A: (OneDimensionalArrayAggregate S) compiling local sums : A -> List S Time: 0.01 SEC.
compiling exported variance : A -> S Time: 0 SEC.
****** Domain: S already in scope augmenting S: (RadicalCategory) augmenting $: (SIGNATURE $ gmean (S A)) augmenting $: (SIGNATURE $ stdev (S A)) augmenting $: (SIGNATURE $ stdize (A A)) compiling exported stdize : A -> A Time: 0.01 SEC.
compiling exported stdize! : A -> A Time: 0 SEC.
compiling exported variance : A -> S Time: 0.01 SEC.
****** Domain: S already in scope augmenting S: (RadicalCategory) augmenting $: (SIGNATURE $ gmean (S A)) augmenting $: (SIGNATURE $ stdev (S A)) augmenting $: (SIGNATURE $ stdize (A A)) compiling exported stdize : A -> A Time: 0 SEC.
****** Domain: A already in scope augmenting A: (shallowlyMutable) augmenting $: (SIGNATURE $ stdize! (A A)) augmenting $: (SIGNATURE $ center! (A A)) compiling exported stdize! : A -> A Time: 0 SEC.
****** Domain: A already in scope augmenting A: (FiniteLinearAggregate S) ****** Domain: S already in scope augmenting S: (OrderedSet) augmenting $: (SIGNATURE $ median (S A)) compiling exported median : A -> S Time: 0.01 SEC.
compiling exported mean : A -> S Time: 0 SEC.
compiling exported hmean : A -> S Time: 0 SEC.
compiling exported moment : (A,Integer) -> S Time: 0 SEC.
compiling exported center : A -> A Time: 0 SEC.
****** Domain: A already in scope augmenting A: (shallowlyMutable) augmenting $: (SIGNATURE $ center! (A A)) compiling exported center! : A -> A Time: 0 SEC.
****** Domain: S already in scope augmenting S: (RadicalCategory) augmenting $: (SIGNATURE $ gmean (S A)) augmenting $: (SIGNATURE $ stdev (S A)) augmenting $: (SIGNATURE $ stdize (A A)) compiling exported gmean : A -> S Time: 0.01 SEC.
compiling exported stdev : A -> S Time: 0 SEC.
****** Domain: A already in scope augmenting A: (FiniteLinearAggregate S) ****** Domain: S already in scope augmenting S: (OrderedSet) augmenting $: (SIGNATURE $ median (S A)) ****** Domain: A already in scope augmenting A: (shallowlyMutable) ****** Domain: S already in scope augmenting S: (Field) augmenting $: (SIGNATURE $ mean (S A)) augmenting $: (SIGNATURE $ hmean (S A)) augmenting $: (SIGNATURE $ moment (S A (Integer))) augmenting $: (SIGNATURE $ variance (S A)) augmenting $: (SIGNATURE $ center (A A)) augmenting $: (SIGNATURE $ center! (A A)) ****** Domain: S already in scope augmenting S: (RadicalCategory) augmenting $: (SIGNATURE $ gmean (S A)) augmenting $: (SIGNATURE $ stdev (S A)) augmenting $: (SIGNATURE $ stdize (A A)) augmenting $: (SIGNATURE $ stdize! (A A)) ****** Domain: A already in scope augmenting A: (shallowlyMutable) ****** Domain: S already in scope augmenting S: (Field) augmenting $: (SIGNATURE $ mean (S A)) augmenting $: (SIGNATURE $ hmean (S A)) augmenting $: (SIGNATURE $ moment (S A (Integer))) augmenting $: (SIGNATURE $ variance (S A)) augmenting $: (SIGNATURE $ center (A A)) augmenting $: (SIGNATURE $ center! (A A)) ****** Domain: S already in scope augmenting S: (Field) augmenting $: (SIGNATURE $ mean (S A)) augmenting $: (SIGNATURE $ hmean (S A)) augmenting $: (SIGNATURE $ moment (S A (Integer))) augmenting $: (SIGNATURE $ variance (S A)) augmenting $: (SIGNATURE $ center (A A)) ****** Domain: S already in scope augmenting S: (RadicalCategory) augmenting $: (SIGNATURE $ gmean (S A)) augmenting $: (SIGNATURE $ stdev (S A)) augmenting $: (SIGNATURE $ stdize (A A)) ****** Domain: S already in scope augmenting S: (Field) augmenting $: (SIGNATURE $ mean (S A)) augmenting $: (SIGNATURE $ hmean (S A)) augmenting $: (SIGNATURE $ moment (S A (Integer))) augmenting $: (SIGNATURE $ variance (S A)) augmenting $: (SIGNATURE $ center (A A)) (time taken in buildFunctor: 0)
;;; *** |StatPackage| REDEFINED
;;; *** |StatPackage| REDEFINED Time: 0 SEC.
Warnings: [1] median: remainder has no value [2] median: quotient has no value
Cumulative Statistics for Constructor StatPackage Time: 0.08 seconds
finalizing NRLIB STAT Processing StatPackage for Browser database: --------constructor--------- --------(median (S A))--------- --------(mean (S A))--------- --------(hmean (S A))--------- --------(moment (S A (Integer)))--------- --------(variance (S A))--------- --------(center (A A))--------- --------(center! (A A))--------- --------(gmean (S A))--------- --------(stdev (S A))--------- --------(stdize (A A))--------- --------(stdize! (A A))--------- ; compiling file "/var/aw/var/LatexWiki/STAT.NRLIB/STAT.lsp" (written 01 JUN 2015 10:24:18 PM):
; /var/aw/var/LatexWiki/STAT.NRLIB/STAT.fasl written ; compilation finished in 0:00:00.154 ------------------------------------------------------------------------ StatPackage is now explicitly exposed in frame initial StatPackage will be automatically loaded when needed from /var/aw/var/LatexWiki/STAT.NRLIB/STAT
IDSTAT abbreviates package IntegralDomainStatPackage ------------------------------------------------------------------------ initializing NRLIB IDSTAT for IntegralDomainStatPackage compiling into NRLIB IDSTAT ****** Domain: A already in scope compiling exported mean : A -> Fraction S Time: 0 SEC.
compiling exported moment : (A,NonNegativeInteger) -> Fraction S Time: 0 SEC.
(time taken in buildFunctor: 0)
;;; *** |IntegralDomainStatPackage| REDEFINED
;;; *** |IntegralDomainStatPackage| REDEFINED Time: 0.01 SEC.
Cumulative Statistics for Constructor IntegralDomainStatPackage Time: 0.01 seconds
finalizing NRLIB IDSTAT Processing IntegralDomainStatPackage for Browser database: --------constructor--------- --------(median (S A))--------- --------(mean (S A))--------- --------(hmean (S A))--------- --------(moment (S A (Integer)))--------- --------(variance (S A))--------- --------(center (A A))--------- --------(center! (A A))--------- --------(gmean (S A))--------- --------(stdev (S A))--------- --------(stdize (A A))--------- --------(stdize! (A A))--------- --------constructor--------- --------(mean ((Fraction S) A))--------- --------(moment ((Fraction S) A (NonNegativeInteger)))--------- --->-->IntegralDomainStatPackage(): Spurious comments: This package exports statistic utilities over IntegralDomain ; compiling file "/var/aw/var/LatexWiki/IDSTAT.NRLIB/IDSTAT.lsp" (written 01 JUN 2015 10:24:18 PM):
; /var/aw/var/LatexWiki/IDSTAT.NRLIB/IDSTAT.fasl written ; compilation finished in 0:00:00.020 ------------------------------------------------------------------------ IntegralDomainStatPackage is now explicitly exposed in frame initial
IntegralDomainStatPackage will be automatically loaded when needed from /var/aw/var/LatexWiki/IDSTAT.NRLIB/IDSTAT
MSTAT abbreviates package MatrixStatPackage ------------------------------------------------------------------------ initializing NRLIB MSTAT for MatrixStatPackage compiling into NRLIB MSTAT importing StatPackage(S,Col) ****** Domain: Col already in scope augmenting Col: (shallowlyMutable) compiling local colReduce : (Col -> S,M) -> Col Time: 0.01 SEC.
****** Domain: S already in scope augmenting S: (OrderedSet) augmenting $: (SIGNATURE $ median (Col M)) compiling exported median : M -> Col Time: 0 SEC.
****** Domain: S already in scope augmenting S: (Field) augmenting $: (SIGNATURE $ mean (Col M)) augmenting $: (SIGNATURE $ hmean (Col M)) augmenting $: (SIGNATURE $ variance (Col M)) augmenting $: (SIGNATURE $ moment (Col M (Integer))) augmenting $: (SIGNATURE $ center (M M)) augmenting $: (SIGNATURE $ center! (M M)) compiling exported mean : M -> Col Time: 0 SEC.
compiling exported hmean : M -> Col Time: 0 SEC.
compiling exported variance : M -> Col Time: 0 SEC.
compiling exported moment : (M,Integer) -> Col Time: 0.01 SEC.
compiling exported center : M -> M Time: 0 SEC.
compiling exported center! : M -> M Time: 0 SEC.
****** Domain: M already in scope augmenting M: (MatrixCategory S Row Col) augmenting $: (SIGNATURE $ cov (M M)) compiling exported cov : M -> M Time: 0.01 SEC.
****** Domain: S already in scope augmenting S: (RadicalCategory) augmenting $: (SIGNATURE $ gmean (Col M)) augmenting $: (SIGNATURE $ stdev (Col M)) augmenting $: (SIGNATURE $ stdize (M M)) augmenting $: (SIGNATURE $ stdize! (M M)) compiling exported gmean : M -> Col Time: 0 SEC.
compiling exported stdev : M -> Col Time: 0 SEC.
compiling exported stdize : M -> M Time: 0.01 SEC.
compiling exported stdize! : M -> M Time: 0 SEC.
****** Domain: M already in scope augmenting M: (MatrixCategory S Row Col) augmenting $: (SIGNATURE $ cor (M M)) augmenting $: (SIGNATURE $ cov (M M)) compiling exported cor : M -> M Time: 0.01 SEC.
****** Domain: Col already in scope augmenting Col: (shallowlyMutable) ****** Domain: M already in scope augmenting M: (MatrixCategory S Row Col) ****** Domain: S already in scope augmenting S: (Field) augmenting $: (SIGNATURE $ mean (Col M)) augmenting $: (SIGNATURE $ hmean (Col M)) augmenting $: (SIGNATURE $ variance (Col M)) augmenting $: (SIGNATURE $ moment (Col M (Integer))) augmenting $: (SIGNATURE $ center (M M)) augmenting $: (SIGNATURE $ center! (M M)) augmenting $: (SIGNATURE $ cov (M M)) ****** Domain: S already in scope augmenting S: (RadicalCategory) augmenting $: (SIGNATURE $ gmean (Col M)) augmenting $: (SIGNATURE $ stdev (Col M)) augmenting $: (SIGNATURE $ stdize (M M)) augmenting $: (SIGNATURE $ stdize! (M M)) augmenting $: (SIGNATURE $ cor (M M)) ****** Domain: Col already in scope augmenting Col: (shallowlyMutable) ****** Domain: M already in scope augmenting M: (MatrixCategory S Row Col) ****** Domain: S already in scope augmenting S: (Field) augmenting $: (SIGNATURE $ mean (Col M)) augmenting $: (SIGNATURE $ hmean (Col M)) augmenting $: (SIGNATURE $ variance (Col M)) augmenting $: (SIGNATURE $ moment (Col M (Integer))) augmenting $: (SIGNATURE $ center (M M)) augmenting $: (SIGNATURE $ center! (M M)) augmenting $: (SIGNATURE $ cov (M M)) ****** Domain: Col already in scope augmenting Col: (shallowlyMutable) ****** Domain: S already in scope augmenting S: (Field) augmenting $: (SIGNATURE $ mean (Col M)) augmenting $: (SIGNATURE $ hmean (Col M)) augmenting $: (SIGNATURE $ variance (Col M)) augmenting $: (SIGNATURE $ moment (Col M (Integer))) augmenting $: (SIGNATURE $ center (M M)) augmenting $: (SIGNATURE $ center! (M M)) ****** Domain: S already in scope augmenting S: (RadicalCategory) augmenting $: (SIGNATURE $ gmean (Col M)) augmenting $: (SIGNATURE $ stdev (Col M)) augmenting $: (SIGNATURE $ stdize (M M)) augmenting $: (SIGNATURE $ stdize! (M M)) ****** Domain: Col already in scope augmenting Col: (shallowlyMutable) ****** Domain: S already in scope augmenting S: (Field) augmenting $: (SIGNATURE $ mean (Col M)) augmenting $: (SIGNATURE $ hmean (Col M)) augmenting $: (SIGNATURE $ variance (Col M)) augmenting $: (SIGNATURE $ moment (Col M (Integer))) augmenting $: (SIGNATURE $ center (M M)) augmenting $: (SIGNATURE $ center! (M M)) ****** Domain: Col already in scope augmenting Col: (shallowlyMutable) ****** Domain: S already in scope augmenting S: (OrderedSet) augmenting $: (SIGNATURE $ median (Col M)) (time taken in buildFunctor: 0)
;;; *** |MatrixStatPackage| REDEFINED
;;; *** |MatrixStatPackage| REDEFINED Time: 0.01 SEC.
Cumulative Statistics for Constructor MatrixStatPackage Time: 0.06 seconds
finalizing NRLIB MSTAT Processing MatrixStatPackage for Browser database: --------constructor--------- --------(median (S A))--------- --------(mean (S A))--------- --------(hmean (S A))--------- --------(moment (S A (Integer)))--------- --------(variance (S A))--------- --------(center (A A))--------- --------(center! (A A))--------- --------(gmean (S A))--------- --------(stdev (S A))--------- --------(stdize (A A))--------- --------(stdize! (A A))--------- --------constructor--------- --------(mean ((Fraction S) A))--------- --------(moment ((Fraction S) A (NonNegativeInteger)))--------- --------constructor--------- --------(median (Col M))--------- --------(mean (Col M))--------- --------(hmean (Col M))--------- --------(variance (Col M))--------- --------(moment (Col M (Integer)))--------- --------(center (M M))--------- --------(center! (M M))--------- --------(cov (M M))--------- --------(gmean (Col M))--------- --------(stdev (Col M))--------- --------(stdize (M M))--------- --------(stdize! (M M))--------- --------(cor (M M))--------- --->-->MatrixStatPackage(): Spurious comments: This package exports statistic utilities over IntegralDomain --->-->MatrixStatPackage(): Spurious comments: This package exports statistic utilities on two dimensional arrays Function are applied column by column ; compiling file "/var/aw/var/LatexWiki/MSTAT.NRLIB/MSTAT.lsp" (written 01 JUN 2015 10:24:18 PM):
; /var/aw/var/LatexWiki/MSTAT.NRLIB/MSTAT.fasl written ; compilation finished in 0:00:00.063 ------------------------------------------------------------------------ MatrixStatPackage is now explicitly exposed in frame initial MatrixStatPackage will be automatically loaded when needed from /var/aw/var/LatexWiki/MSTAT.NRLIB/MSTAT

And

fricas
a:= ["a","c","d","g","z","a","d","g","f"]

\label{eq1}\begin{array}{@{}l}
\displaystyle
\left[ \verb#"a"# , \: \verb#"c"# , \: \verb#"d"# , \: \verb#"g"# , \: \verb#"z"# , \: \right.
\
\
\displaystyle
\left.\verb#"a"# , \: \verb#"d"# , \: \verb#"g"# , \: \verb#"f"# \right] 
(1)
Type: List(String)
fricas
b:= [1,7,8,9,2,4,6,17,18,14,32]

\label{eq2}\left[ 1, \: 7, \: 8, \: 9, \: 2, \: 4, \: 6, \:{17}, \:{18}, \:{14}, \:{32}\right](2)
Type: List(PositiveInteger)
fricas
median a

\label{eq3}\verb#"d"#(3)
Type: String
fricas
median b

\label{eq4}8(4)
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mean b

\label{eq5}{118}\over{11}(5)
Type: Fraction(Integer)
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hmean b

\label{eq6}{125664}\over{28705}(6)
Type: Fraction(Integer)
fricas
moment(b,1)

\label{eq7}{118}\over{11}(7)
Type: Fraction(Integer)
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moment(b,2)

\label{eq8}{2084}\over{11}(8)
Type: Fraction(Integer)
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moment(b,3)

\label{eq9}{48130}\over{11}(9)
Type: Fraction(Integer)
fricas
variance b

\label{eq10}{900}\over{11}(10)
Type: Fraction(Integer)
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stdev b

\label{eq11}{30}\over{\sqrt{11}}(11)
Type: AlgebraicNumber?
fricas
gmean b

\label{eq12}2 \ {\root{11}\of{1619352}}(12)
Type: AlgebraicNumber?
fricas
center b

\label{eq13}\begin{array}{@{}l}
\displaystyle
\left[ -{{107}\over{11}}, \: -{{41}\over{11}}, \: -{{30}\over{1
1}}, \: -{{19}\over{11}}, \: -{{96}\over{11}}, \: -{{74}\over{1
1}}, \: -{{52}\over{11}}, \:{{69}\over{11}}, \:{{80}\over{11}}, \:{{36}\over{11}}, \right.
\
\
\displaystyle
\left.\:{{234}\over{11}}\right] 
(13)
Type: List(Fraction(Integer))
fricas
stdize b

\label{eq14}\begin{array}{@{}l}
\displaystyle
\left[ -{{{107}\ {\sqrt{11}}}\over{330}}, \: -{{{41}\ {\sqrt{1
1}}}\over{330}}, \: -{{\sqrt{11}}\over{11}}, \: -{{{19}\ {\sqrt{1
1}}}\over{330}}, \: -{{{16}\ {\sqrt{11}}}\over{55}}, \: \right.
\
\
\displaystyle
\left.-{{{37}\ {\sqrt{11}}}\over{165}}, \: -{{{26}\ {\sqrt{11}}}\over{1
65}}, \:{{{23}\ {\sqrt{11}}}\over{110}}, \:{{8 \ {\sqrt{11}}}\over{3
3}}, \:{{6 \ {\sqrt{11}}}\over{55}}, \:{{{39}\ {\sqrt{11}}}\over{5
5}}\right] 
(14)
Type: List(AlgebraicNumber?)
fricas
c := [3+7*%i,5+8*%i,8+3*%i,4+5*%i]

\label{eq15}\left[{3 +{7 \  i}}, \:{5 +{8 \  i}}, \:{8 +{3 \  i}}, \:{4 +{5 \  i}}\right](15)
Type: List(Complex(Integer))
fricas
mean c

\label{eq16}{{20}+{{23}\  i}}\over 4(16)
Type: Fraction(Complex(Integer))




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