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R Software Module: rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Wed, 19 Dec 2007 09:17:31 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Dec/19/t1198079999rvbsc80ddpxkrbl.htm/, Retrieved Wed, 19 Dec 2007 16:59:59 +0100
 
User-defined keywords:
 
Dataseries X:
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-0.000312453179218713 0.0262356302140672 -0.00240963773602199 -0.0401718968445318 0.0296358908444879 0.0343859545201239 -2.01712740474642e-06 0.00235757739993286 0.0339545629792695 -0.00683912157376615 0.00363863561455776 0.0126118170620050 -0.0231634434966821 -0.000806067760311788 -0.0799379801949807 -0.0283672069388685 0.0229685809594173 0.0126991579481110 0.044980294248654 -0.00408052292768904 0.0121499692425831 0.0171948557772712 -0.00494342185632396 -0.00694750482277671 -0.0198733208229558 0.0116892757062565 -0.00695206652392818 0.0492740258727255 0.00043041287794735 0.0286373927224382 -0.0198599774361160 -0.0233359397182088 0.058885928618586 -0.0368077914615597 -0.0295494248192446 -0.0226291731883809 0.0108895152505279 -0.00683342890962535 0.0289472144392165 -0.0183679090036504 0.0312576150959544 0.0190412653012111 -0.00144515233700617 0.0284447147991525 -0.0298542363688031 -0.0477652688245287 0.0181613687717107 -0.0228998044806201 -0.0248428499898979 -0.0158024801405908 0.0341677916473078 0.00380975133031554 -0.00849468570564401 0.000789066487181422 -0.0305920534281536 -0.106754928751708 -0.0164284059659585 0.00414366263453509 0.0225748086657257 -0.0304004402854452 0.0132026598217524 0.0402412167422170 -0.0292894617179887 0.0231998070498554 -0.0107942982530465 -0.0098567569534148 -0.0345339066023613
 
Text written by user:
 
Output produced by software:


Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-0.001811113664213670.00355124301406040-0.509994291306717
Geometric MeanNaN
Harmonic Mean-0.000134674084536832
Quadratic Mean0.0289072259317450
Winsorized Mean ( 1 / 22 )-0.001554321935693270.00335516481928701-0.463262468287197
Winsorized Mean ( 2 / 22 )-0.0007221135850550420.00304048654843851-0.237499352011899
Winsorized Mean ( 3 / 22 )-0.0005943093548956430.00291892083135335-0.203605849296054
Winsorized Mean ( 4 / 22 )-0.0007430351363357030.00280848173747193-0.264568263493339
Winsorized Mean ( 5 / 22 )-0.000589623047799710.00277314435317179-0.212618952607111
Winsorized Mean ( 6 / 22 )-0.0002557163756054350.00270676379289044-0.0944731033705628
Winsorized Mean ( 7 / 22 )-0.0005174677664150910.00265077275116135-0.195213930046768
Winsorized Mean ( 8 / 22 )-0.0006458881049015860.00260502107415751-0.247939685136894
Winsorized Mean ( 9 / 22 )-0.0006974520407436180.00258188298831926-0.270133094295510
Winsorized Mean ( 10 / 22 )-0.0007048936251499460.0025672992019126-0.274566215197983
Winsorized Mean ( 11 / 22 )-0.0005851123503114470.00253648044517194-0.230678833509313
Winsorized Mean ( 12 / 22 )-0.0003495411806603480.00236650943867602-0.147703269189539
Winsorized Mean ( 13 / 22 )-0.0006461959210005730.00222289252630989-0.290700478476704
Winsorized Mean ( 14 / 22 )-0.0006584678339074330.00220948326967691-0.298018927295938
Winsorized Mean ( 15 / 22 )-0.0006876021497946560.00218613685030269-0.314528411018483
Winsorized Mean ( 16 / 22 )-0.001466805032726100.00204379585231982-0.717686666729061
Winsorized Mean ( 17 / 22 )-0.0009908162385362460.00190228345014527-0.520856257494425
Winsorized Mean ( 18 / 22 )-0.001246891655503330.00186245590265719-0.669487880880492
Winsorized Mean ( 19 / 22 )-0.001955883042637820.00163335316112153-1.19746487728033
Winsorized Mean ( 20 / 22 )-0.001527225978742150.00152520296017896-1.00132639302178
Winsorized Mean ( 21 / 22 )-0.001358415773898930.00149242072313816-0.91020966999342
Winsorized Mean ( 22 / 22 )0.0001344103380218600.001239118406257970.108472553827820
Trimmed Mean ( 1 / 22 )-0.001130394082602980.00314091458533788-0.359893289642379
Trimmed Mean ( 2 / 22 )-0.0006795501753482280.0028745660757796-0.236400958417326
Trimmed Mean ( 3 / 22 )-0.0006561751880502240.00276462166707333-0.237347191431391
Trimmed Mean ( 4 / 22 )-0.000679593328283880.00268879449327551-0.252750193435570
Trimmed Mean ( 5 / 22 )-0.0006609503408300540.00263750222433876-0.250597074281429
Trimmed Mean ( 6 / 22 )-0.0006783282631319920.00258488556552971-0.262421003149122
Trimmed Mean ( 7 / 22 )-0.0007673691325165190.00253779577993576-0.302376234755952
Trimmed Mean ( 8 / 22 )-0.00081426938889970.00249280786241283-0.32664747298717
Trimmed Mean ( 9 / 22 )-0.0008430488430524390.00244630775024805-0.344620926360126
Trimmed Mean ( 10 / 22 )-0.0008661102750966250.00239137933135267-0.362180212792387
Trimmed Mean ( 11 / 22 )-0.0008901136429775750.0023230780365403-0.38316131829269
Trimmed Mean ( 12 / 22 )-0.000933316785913370.00224099603862590-0.416474090014744
Trimmed Mean ( 13 / 22 )-0.001012814683376690.00217521650801476-0.465615574194519
Trimmed Mean ( 14 / 22 )-0.001061263316668990.00212229110326385-0.500055489577696
Trimmed Mean ( 15 / 22 )-0.001113362346292590.00205207448778117-0.542554548054653
Trimmed Mean ( 16 / 22 )-0.001167697457083760.00196035991540133-0.595654628474031
Trimmed Mean ( 17 / 22 )-0.001129742518507930.00187288730269852-0.6032090221767
Trimmed Mean ( 18 / 22 )-0.001147404872887640.00179025439981809-0.640917219923729
Trimmed Mean ( 19 / 22 )-0.001134635496574890.00168083094063132-0.675044389740187
Trimmed Mean ( 20 / 22 )-0.001027377045139770.00159736341775679-0.643170510679742
Trimmed Mean ( 21 / 22 )-0.0009603972880370550.00150857573542661-0.636625172660267
Trimmed Mean ( 22 / 22 )-0.0009051856140148080.00137805923590635-0.656855373433543
Median-0.000806067760311788
Midrange-0.023934500066561
Midmean - Weighted Average at Xnp-0.00176207871468067
Midmean - Weighted Average at X(n+1)p-0.00116769745708376
Midmean - Empirical Distribution Function-0.00116769745708376
Midmean - Empirical Distribution Function - Averaging-0.00116769745708376
Midmean - Empirical Distribution Function - Interpolation-0.00112974251850793
Midmean - Closest Observation-0.00176207871468067
Midmean - True Basic - Statistics Graphics Toolkit-0.00116769745708376
Midmean - MS Excel (old versions)-0.00116769745708376
Number of observations67
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/19/t1198079999rvbsc80ddpxkrbl/1vbz91198081045.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/19/t1198079999rvbsc80ddpxkrbl/1vbz91198081045.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/19/t1198079999rvbsc80ddpxkrbl/2scxj1198081045.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/19/t1198079999rvbsc80ddpxkrbl/2scxj1198081045.ps (open in new window)


 
Parameters (Session):
 
Parameters (R input):
 
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('http://www.xycoon.com/winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
 




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