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Central Tendency - Totale Uitvoer van België

*The author of this computation has been verified*
R Software Module: rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Wed, 10 Dec 2008 07:45:06 -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/Dec/10/t1228920364miurpfq5xir1tzq.htm/, Retrieved Wed, 10 Dec 2008 14:46:06 +0000
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Dec/10/t1228920364miurpfq5xir1tzq.htm/},
    year = {2008},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
 
Feedback Forum:
2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc] [reply] 
test

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Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
18 562,2 23 184,8 22 925,8 21 490,2 23 243,2 21 688,7 21 423,1 21 211,2 17 877,4 20 664,3 22 160,0 19 813,6 17 735,4 19 640,2 20 844,4 19 823,1 18 594,6 21 350,6 18 574,1 18 924,2 17 343,4 19 961,2 19 932,1 19 464,6 16 165,4 17 574,9 19 795,4 19 439,5 17 170,0 21 072,4 17 751,8 17 515,5 18 040,3 19 090,1 17 746,5 19 202,1 15 141,6 16 258,1 18 586,5 17 209,4 17 838,7 19 123,5 16 583,6 15 991,2 16 704,4 17 420,4 17 872,0 17 823,2 13 866,5 15 912,8 17 870,5 15 420,3 16 379,4 17 903,9 15 305,8 14 583,3 14 861,0 14 968,9 16 726,5 16 283,6 11 703,7 15 101,8 15 469,7 14 956,9 15 370,6 15 998,1 14 725,1 14 768,9 13 659,6 15 070,3 16 943,0 15 761,3 12 083,0 15 023,6 15 106,5 15 498,6 15 258,9 15 859,4 14 205,3 14 291,1 12 875,1 14 755,3 15 873,2 14 803,0 12 520,2 14 568,3 15 644,8 15 454,9 14 254,0 16 754,8 14 944,2 15 044,5
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean17151.9467391304269.78453965031363.5764627630712
Geometric Mean16962.3275394395
Harmonic Mean16776.011277075
Quadratic Mean17343.9497648284
Winsorized Mean ( 1 / 30 )17155.4347826087268.74244389842163.8359707300016
Winsorized Mean ( 2 / 30 )17159.3086956522265.47758989217064.6356202895387
Winsorized Mean ( 3 / 30 )17145.9097826087257.65653751380366.5456034923629
Winsorized Mean ( 4 / 30 )17159.5271739130247.63948231048469.2923721767391
Winsorized Mean ( 5 / 30 )17159.9836956522243.79416363864170.387180068376
Winsorized Mean ( 6 / 30 )17177.7032608696239.79530160809771.6348616744103
Winsorized Mean ( 7 / 30 )17175.8923913043238.22544039139672.0993205557097
Winsorized Mean ( 8 / 30 )17166.9967391304235.48038661082472.9020237575123
Winsorized Mean ( 9 / 30 )17180.5358695652229.41541338407974.8883242679172
Winsorized Mean ( 10 / 30 )17157.3836956522224.66531686424976.3686355113696
Winsorized Mean ( 11 / 30 )17152.8043478261218.7217435161678.422949964089
Winsorized Mean ( 12 / 30 )17065.0347826087202.92010249538884.0973100878292
Winsorized Mean ( 13 / 30 )17062.8445652174202.03670262541484.4541825494586
Winsorized Mean ( 14 / 30 )17051.4467391304198.82558731743785.7608267084192
Winsorized Mean ( 15 / 30 )17059.3543478261197.42202471326586.4105936133673
Winsorized Mean ( 16 / 30 )17070.6586956522195.18506665834387.4588358008612
Winsorized Mean ( 17 / 30 )17044.3271739130190.55648066823089.4450144867455
Winsorized Mean ( 18 / 30 )17012.3184782609185.20068561829491.858830983617
Winsorized Mean ( 19 / 30 )17018.4315217391183.08572212434892.9533517101928
Winsorized Mean ( 20 / 30 )16971.3663043478175.17536388835996.8821524193543
Winsorized Mean ( 21 / 30 )16959.3141304348171.96793501311498.619048540308
Winsorized Mean ( 22 / 30 )16958.8597826087169.95847071546799.7823745484277
Winsorized Mean ( 23 / 30 )16918.5597826087164.17381935013103.052726979122
Winsorized Mean ( 24 / 30 )16841.7336956522151.816880653958110.934526009925
Winsorized Mean ( 25 / 30 )16871.4076086957147.662278682502114.2567198558
Winsorized Mean ( 26 / 30 )16881.1576086957145.631685960325115.916790342554
Winsorized Mean ( 27 / 30 )16896.6826086956142.938976682240118.209063761928
Winsorized Mean ( 28 / 30 )16752.9695652174121.664356841300137.698254444974
Winsorized Mean ( 29 / 30 )16720.8804347826115.427780045399144.860105844590
Winsorized Mean ( 30 / 30 )16717.0652173913113.876056884951146.800527474187
Trimmed Mean ( 1 / 30 )17144.8022222222260.25862616698565.8760190765854
Trimmed Mean ( 2 / 30 )17133.6863636364250.50614309904768.3962722497466
Trimmed Mean ( 3 / 30 )17119.9813953488241.28885778943270.9522252796651
Trimmed Mean ( 4 / 30 )17110.5154761905234.12357625858473.0832654687125
Trimmed Mean ( 5 / 30 )17096.7682926829229.31698429464974.5551767361257
Trimmed Mean ( 6 / 30 )17082.22875224.85025950614475.9715767618816
Trimmed Mean ( 7 / 30 )17063.4602564103220.63727271630177.3371608810208
Trimmed Mean ( 8 / 30 )17044.0171052632216.05536841028978.8872650129969
Trimmed Mean ( 9 / 30 )17024.9054054054211.26396374322180.5859414154425
Trimmed Mean ( 10 / 30 )17002.8097222222206.81478835649382.212736610082
Trimmed Mean ( 11 / 30 )16982.4942857143202.47513663669583.8744675904887
Trimmed Mean ( 12 / 30 )16961.5470588235198.39688623188785.4930104044013
Trimmed Mean ( 13 / 30 )16961.5470588235196.38647773072586.3682024079087
Trimmed Mean ( 14 / 30 )16936.9953125194.02935957767787.2908891178374
Trimmed Mean ( 15 / 30 )16924.8645161290191.64297442432388.3145576662524
Trimmed Mean ( 16 / 30 )16911.1166666667188.87561781921889.5357318320097
Trimmed Mean ( 17 / 30 )16895.3185.76341014662890.950634393846
Trimmed Mean ( 18 / 30 )16880.8982142857182.67502696650992.4094469540197
Trimmed Mean ( 19 / 30 )16868.4592592593179.71996841655893.8596829716843
Trimmed Mean ( 20 / 30 )16854.4942307692176.2871271382995.6081961534694
Trimmed Mean ( 21 / 30 )16843.742173.35052666378797.1657965174137
Trimmed Mean ( 22 / 30 )16833.19375170.10082360109898.9600955106215
Trimmed Mean ( 23 / 30 )16821.7695652174166.19993340394101.214057194193
Trimmed Mean ( 24 / 30 )16812.9704545455162.259148052224103.618012644403
Trimmed Mean ( 25 / 30 )16810.3452380952159.566526643638105.350073049080
Trimmed Mean ( 26 / 30 )16810.3452380952156.651033002867107.310784460563
Trimmed Mean ( 27 / 30 )16797.6105263158152.975012918369109.806237017802
Trimmed Mean ( 28 / 30 )16788.2333333333148.401546487899113.127078057116
Trimmed Mean ( 29 / 30 )16791.6411764706147.195095724367114.077450025333
Trimmed Mean ( 30 / 30 )16798.65625146.477886689638114.683906421954
Median16740.65
Midrange17473.45
Midmean - Weighted Average at Xnp16785.1744680851
Midmean - Weighted Average at X(n+1)p16821.7695652174
Midmean - Empirical Distribution Function16785.1744680851
Midmean - Empirical Distribution Function - Averaging16821.7695652174
Midmean - Empirical Distribution Function - Interpolation16821.7695652174
Midmean - Closest Observation16785.1744680851
Midmean - True Basic - Statistics Graphics Toolkit16821.7695652174
Midmean - MS Excel (old versions)16833.19375
Number of observations92
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t1228920364miurpfq5xir1tzq/13rpp1228920304.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t1228920364miurpfq5xir1tzq/13rpp1228920304.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t1228920364miurpfq5xir1tzq/2wl0p1228920304.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t1228920364miurpfq5xir1tzq/2wl0p1228920304.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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