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CVWS1WLQ1

R Software Module: rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Sun, 06 Jan 2008 06:23:42 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Jan/06/t1199625912wa1bpsqv4s6rgj5.htm/, Retrieved Sun, 06 Jan 2008 14:25:12 +0100
 
User-defined keywords:
Investigating associations Werkloosheidsgraad BE Q1
 
Dataseries X:
» Textbox « » Textfile « » CSV «
8,1 7,9 7,8 7,7 7,3 7,2 7,1 6,9 6,8 6,7 6,8 6,8 6,7 6,8 6,8 6,7 6,3 6,2 6,2 6,5 6,5 6,4 6,2 6,2 6,3 7,5 7,4 7,4 7,4 7,4 7,4 7,2 7,2 7,2 7,5 7,4 7,5 8,0 8,0 8,0 8,1 8,1 8,1 7,9 7,9 8,0 8,2 8,1 8,2 8,5 8,5 8,6 8,4 8,4 8,4 7,7 7,8 7,9 8,8 8,8 8,9 8,5 8,5 8,5 8,4 8,5 8,4 8,3 8,4 8,4 8,5 8,5 8,5 8,5 8,5 8,5 8,5 8,5 8,5 8,3 8,3 8,3 8,2 8,1 8,1 8,2 8,0 7,9 7,9 7,8 7,7 7,9 7,7 7,6 7,6 7,5 7,4 7,3 7,3
 
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 time15 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.739393939393940.071570107706259108.137240356802
Geometric Mean7.7054612941712
Harmonic Mean7.67002112349813
Quadratic Mean7.77175668817559
Winsorized Mean ( 1 / 33 )7.738383838383840.0714099120029983108.365682316748
Winsorized Mean ( 2 / 33 )7.738383838383840.0714099120029983108.365682316748
Winsorized Mean ( 3 / 33 )7.732323232323230.0705695573597417109.570238522345
Winsorized Mean ( 4 / 33 )7.732323232323230.0692127936708729111.718120627997
Winsorized Mean ( 5 / 33 )7.732323232323230.0692127936708729111.718120627997
Winsorized Mean ( 6 / 33 )7.738383838383840.0679636829109472113.860572396046
Winsorized Mean ( 7 / 33 )7.745454545454550.0665780599672423116.336441002719
Winsorized Mean ( 8 / 33 )7.745454545454550.0665780599672423116.336441002719
Winsorized Mean ( 9 / 33 )7.763636363636360.0632790273545398122.688933256484
Winsorized Mean ( 10 / 33 )7.763636363636360.0632790273545398122.688933256484
Winsorized Mean ( 11 / 33 )7.763636363636360.0632790273545398122.688933256484
Winsorized Mean ( 12 / 33 )7.775757575757580.0612534991211813126.943891978715
Winsorized Mean ( 13 / 33 )7.775757575757580.0612534991211813126.943891978715
Winsorized Mean ( 14 / 33 )7.775757575757580.0612534991211813126.943891978715
Winsorized Mean ( 15 / 33 )7.775757575757580.0612534991211813126.943891978715
Winsorized Mean ( 16 / 33 )7.775757575757580.0612534991211813126.943891978715
Winsorized Mean ( 17 / 33 )7.79292929292930.0585197132979158133.167591803749
Winsorized Mean ( 18 / 33 )7.829292929292930.0531283267163138147.365697607955
Winsorized Mean ( 19 / 33 )7.829292929292930.0480982924162506162.776941466797
Winsorized Mean ( 20 / 33 )7.829292929292930.0480982924162506162.776941466797
Winsorized Mean ( 21 / 33 )7.829292929292930.0480982924162506162.776941466797
Winsorized Mean ( 22 / 33 )7.829292929292930.0480982924162506162.776941466797
Winsorized Mean ( 23 / 33 )7.852525252525250.0450918902916601174.144956038306
Winsorized Mean ( 24 / 33 )7.852525252525250.0450918902916601174.144956038306
Winsorized Mean ( 25 / 33 )7.852525252525250.0450918902916601174.144956038306
Winsorized Mean ( 26 / 33 )7.852525252525250.0386950462660495202.933605468123
Winsorized Mean ( 27 / 33 )7.852525252525250.0386950462660495202.933605468123
Winsorized Mean ( 28 / 33 )7.852525252525250.0386950462660495202.933605468123
Winsorized Mean ( 29 / 33 )7.852525252525250.0386950462660495202.933605468123
Winsorized Mean ( 30 / 33 )7.822222222222220.0352438147796421221.945957641923
Winsorized Mean ( 31 / 33 )7.822222222222220.0352438147796421221.945957641923
Winsorized Mean ( 32 / 33 )7.822222222222220.0352438147796421221.945957641923
Winsorized Mean ( 33 / 33 )7.855555555555560.0312662152437971251.247408562314
Trimmed Mean ( 1 / 33 )7.743298969072160.0702674569010762110.197512626269
Trimmed Mean ( 2 / 33 )7.748421052631580.0689687784646049112.346792637601
Trimmed Mean ( 3 / 33 )7.753763440860220.067489530290924114.888389464802
Trimmed Mean ( 4 / 33 )7.761538461538460.0661475988758723117.336662153122
Trimmed Mean ( 5 / 33 )7.769662921348310.0650568325123691119.428853531581
Trimmed Mean ( 6 / 33 )7.778160919540230.0637931636527984121.927812858973
Trimmed Mean ( 7 / 33 )7.785882352941180.0626482095079815124.279407409868
Trimmed Mean ( 8 / 33 )7.792771084337350.0616356334850602126.432887012125
Trimmed Mean ( 9 / 33 )7.80.0604509800388242129.030166177463
Trimmed Mean ( 10 / 33 )7.805063291139240.0597218135623897130.690326123226
Trimmed Mean ( 11 / 33 )7.810389610389610.0588562789402438132.702742188636
Trimmed Mean ( 12 / 33 )7.8160.0578298217902173135.155180459543
Trimmed Mean ( 13 / 33 )7.820547945205480.0569706760570891137.273216441537
Trimmed Mean ( 14 / 33 )7.825352112676060.055943285086903139.880096431950
Trimmed Mean ( 15 / 33 )7.83043478260870.0547140262733464143.115674644168
Trimmed Mean ( 16 / 33 )7.835820895522390.0532397482519146147.179901348249
Trimmed Mean ( 17 / 33 )7.841538461538460.0514637805651623152.370043075434
Trimmed Mean ( 18 / 33 )7.846031746031750.0498243405325172157.473870445132
Trimmed Mean ( 19 / 33 )7.847540983606560.0487889711053014160.846617705243
Trimmed Mean ( 20 / 33 )7.849152542372880.0483130306096166162.464503744266
Trimmed Mean ( 21 / 33 )7.850877192982460.0476991148529408164.591674650299
Trimmed Mean ( 22 / 33 )7.852727272727270.0469152502938183167.381122844867
Trimmed Mean ( 23 / 33 )7.854716981132080.0459195704486397171.053799162112
Trimmed Mean ( 24 / 33 )7.854901960784310.0451849120653618173.839044976382
Trimmed Mean ( 25 / 33 )7.855102040816330.0442301133769177177.596244754725
Trimmed Mean ( 26 / 33 )7.855319148936170.0429926429863945182.713101667699
Trimmed Mean ( 27 / 33 )7.855319148936170.0425874685836003184.451422218627
Trimmed Mean ( 28 / 33 )7.855813953488370.0420017303843032187.035483576749
Trimmed Mean ( 29 / 33 )7.856097560975610.0411790824960578190.778839274229
Trimmed Mean ( 30 / 33 )7.856410256410260.0400396011449892196.215996956639
Trimmed Mean ( 31 / 33 )7.859459459459460.0392228290949812200.379718669124
Trimmed Mean ( 32 / 33 )7.862857142857140.038037070437811206.715634310286
Trimmed Mean ( 33 / 33 )7.866666666666670.0363241578628389216.568452773810
Median7.9
Midrange7.55
Midmean - Weighted Average at Xnp7.89298245614035
Midmean - Weighted Average at X(n+1)p7.89298245614035
Midmean - Empirical Distribution Function7.89298245614035
Midmean - Empirical Distribution Function - Averaging7.89298245614035
Midmean - Empirical Distribution Function - Interpolation7.89298245614035
Midmean - Closest Observation7.89298245614035
Midmean - True Basic - Statistics Graphics Toolkit7.89298245614035
Midmean - MS Excel (old versions)7.89298245614035
Number of observations99
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/06/t1199625912wa1bpsqv4s6rgj5/1hzj31199625804.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/06/t1199625912wa1bpsqv4s6rgj5/1hzj31199625804.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/06/t1199625912wa1bpsqv4s6rgj5/27bh31199625804.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/06/t1199625912wa1bpsqv4s6rgj5/27bh31199625804.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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