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Paper_EDAres_output12

R Software Module: rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Thu, 13 Dec 2007 06:06:53 -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/13/t1197550639asmr55apr9kvkh3.htm/, Retrieved Thu, 13 Dec 2007 13:57:19 +0100
 
User-defined keywords:
 
Dataseries X:
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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 time6 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-182.137441327565260.749519289596-0.698514964951013
Geometric MeanNaN
Harmonic Mean-1421.27514245311
Quadratic Mean2382.51336360219
Winsorized Mean ( 1 / 28 )-167.779816814027254.87274868872-0.658288568225625
Winsorized Mean ( 2 / 28 )-162.786786025499247.527576539425-0.657651112257269
Winsorized Mean ( 3 / 28 )-149.630587675492234.577352325179-0.63787312028345
Winsorized Mean ( 4 / 28 )-128.298367046779226.057030091208-0.567548671213692
Winsorized Mean ( 5 / 28 )-119.571668959665222.867594204126-0.536514379251335
Winsorized Mean ( 6 / 28 )-121.546620705288222.096251166054-0.547270023996988
Winsorized Mean ( 7 / 28 )-108.555503330446219.286882922369-0.495038745061996
Winsorized Mean ( 8 / 28 )-109.760246742820218.027689959667-0.503423426460762
Winsorized Mean ( 9 / 28 )-172.608421149171206.478279330166-0.83596406222063
Winsorized Mean ( 10 / 28 )-139.788548114272197.533835418328-0.707668880211001
Winsorized Mean ( 11 / 28 )-125.195166648305193.915031942812-0.645618678418009
Winsorized Mean ( 12 / 28 )-98.0270049449016188.128665516049-0.521063627789032
Winsorized Mean ( 13 / 28 )-119.753868153999182.598244118218-0.655832528578249
Winsorized Mean ( 14 / 28 )-115.505833081639178.516816064141-0.647030546635664
Winsorized Mean ( 15 / 28 )-128.957941034582170.616027992545-0.755837200947014
Winsorized Mean ( 16 / 28 )-104.838421132517162.056718408214-0.646924250733216
Winsorized Mean ( 17 / 28 )-90.9446571445178157.970640749859-0.575706072424719
Winsorized Mean ( 18 / 28 )-83.9055042907007146.763834794335-0.571704224056834
Winsorized Mean ( 19 / 28 )-14.9682237407603134.249865900675-0.111495260277091
Winsorized Mean ( 20 / 28 )21.3963827448587128.8812672809060.166016234913518
Winsorized Mean ( 21 / 28 )22.9239974603962126.1437170954840.181729205292436
Winsorized Mean ( 22 / 28 )-30.8316113258972117.922741098313-0.261456026536839
Winsorized Mean ( 23 / 28 )-4.50065129575653112.962649295775-0.0398419417729155
Winsorized Mean ( 24 / 28 )-57.2982395360851105.393314544034-0.543661045142913
Winsorized Mean ( 25 / 28 )-12.646574882376898.806650045063-0.127993155082264
Winsorized Mean ( 26 / 28 )-11.399418971586598.525447697549-0.115700250422410
Winsorized Mean ( 27 / 28 )-40.459105422558591.963387680426-0.439947966718608
Winsorized Mean ( 28 / 28 )-6.9292186921214987.1241295623657-0.079532716446382
Trimmed Mean ( 1 / 28 )-150.963686359902243.545435623173-0.619858409473464
Trimmed Mean ( 2 / 28 )-133.306749383071230.224702941504-0.579028869099862
Trimmed Mean ( 3 / 28 )-117.432883498686219.294623583749-0.53550279336346
Trimmed Mean ( 4 / 28 )-105.570571433547212.414849524984-0.497001841771565
Trimmed Mean ( 5 / 28 )-99.1207915973596207.413576752765-0.477889601776216
Trimmed Mean ( 6 / 28 )-94.3489202128216202.491775891335-0.465939516790317
Trimmed Mean ( 7 / 28 )-88.9093801143284196.875861340048-0.451601224798007
Trimmed Mean ( 8 / 28 )-85.442417193837190.912932704114-0.447546512347908
Trimmed Mean ( 9 / 28 )-81.5736715837715184.086003079110-0.443128050038198
Trimmed Mean ( 10 / 28 )-68.297770605484178.463427229041-0.382698974607444
Trimmed Mean ( 11 / 28 )-58.6119233300998173.620059267183-0.337587278667508
Trimmed Mean ( 12 / 28 )-50.1376923623283168.490054269530-0.297570634538012
Trimmed Mean ( 13 / 28 )-44.3579477402936163.420090720478-0.271435094330999
Trimmed Mean ( 14 / 28 )-35.6584184617891158.277479261013-0.225290538036591
Trimmed Mean ( 15 / 28 )-26.7864835040279152.727262573359-0.175387701270175
Trimmed Mean ( 16 / 28 )-15.7834034622759147.392418366132-0.107084228871725
Trimmed Mean ( 17 / 28 )-6.43262660690054142.462941386163-0.0451529818513584
Trimmed Mean ( 18 / 28 )2.26714124256006137.0537731945610.0165419834107131
Trimmed Mean ( 19 / 28 )11.0092936879633132.5140689688140.08308018743696
Trimmed Mean ( 20 / 28 )13.6194748650121129.3288160300070.105308896215768
Trimmed Mean ( 21 / 28 )12.8417840770274126.2270768388870.101735573686923
Trimmed Mean ( 22 / 28 )11.8335627386906122.6322360574680.09649634646754
Trimmed Mean ( 23 / 28 )16.1204941040319119.6015834178250.134784955544572
Trimmed Mean ( 24 / 28 )18.2124943619815116.5536849186350.156258417524039
Trimmed Mean ( 25 / 28 )25.9856581456060113.9987292945630.227946910517409
Trimmed Mean ( 26 / 28 )30.0420426135442111.966730660940.26831222485649
Trimmed Mean ( 27 / 28 )34.504969245789108.8359926364860.317036381163318
Trimmed Mean ( 28 / 28 )42.8343108756054105.9336750576520.404350277211603
Median82.6272546138217
Midrange-1460.26139500177
Midmean - Weighted Average at Xnp-20.4925840984222
Midmean - Weighted Average at X(n+1)p12.8417840770274
Midmean - Empirical Distribution Function-20.4925840984222
Midmean - Empirical Distribution Function - Averaging12.8417840770274
Midmean - Empirical Distribution Function - Interpolation12.8417840770274
Midmean - Closest Observation-20.4925840984222
Midmean - True Basic - Statistics Graphics Toolkit12.8417840770274
Midmean - MS Excel (old versions)13.6194748650122
Number of observations84
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197550639asmr55apr9kvkh3/1pu1e1197551199.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197550639asmr55apr9kvkh3/1pu1e1197551199.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197550639asmr55apr9kvkh3/2edvi1197551199.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197550639asmr55apr9kvkh3/2edvi1197551199.ps (open in new window)


 
Parameters:
par1 = -0.4 ; par2 = 1 ; par3 = 1 ; par4 = 12 ;
 
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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