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Vermeulennickopgave5centraltendency2

*Unverified author*
R Software Module: rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Mon, 03 Aug 2009 03:10:49 -0600
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Aug/03/t1249290678vmfejd6bpiq3bll.htm/, Retrieved Mon, 03 Aug 2009 11:11:20 +0200
 
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/2009/Aug/03/t1249290678vmfejd6bpiq3bll.htm/},
    year = {2009},
}
@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 = {2009},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
Roze Garnalen
 
Dataseries X:
» Textbox « » Textfile « » CSV «
106,61 107,86 108,07 109,68 108,57 108,08 109,8 110,7 110,72 109,85 109,71 110 110,87 111,16 110,63 110,26 110,79 111,75 111,75 112,31 112,29 111,86 111,22 112,42 111,94 112,77 113,99 114,22 112,38 114,98 115,94 117,63 117,76 118,11 120,88 121,87 122,34 122,42 122,17 121,99 124,96 125,94 126,59 127,11 125,44 125,53 125,35 124,3 123,62 124 124,47 126,89 124,87 124,55 125,31 126,02 125,31 125,3 123,83 124,49 124,92 125,77 127,27 127,35 126,05 126,84 127,75 126,78 126,98 127,89 127,9 128,06 125,39 128,13 127,97 127,56 126,89 127,8 128,05 128,98 128,55 129,35 129,97 130,89 129,8 132,32 131,1 131,44 132,55 133,35 132,53 131,11 130,02 128,91 129,98 130,91
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean121.5556250.806046187519347150.804788710799
Geometric Mean121.296026907054
Harmonic Mean121.031157473415
Quadratic Mean121.809246211033
Winsorized Mean ( 1 / 32 )121.56031250.802362512859502151.502980949069
Winsorized Mean ( 2 / 32 )121.5642708333330.801521630542737151.666862379020
Winsorized Mean ( 3 / 32 )121.5580208333330.80052937008198151.847046937060
Winsorized Mean ( 4 / 32 )121.5417708333330.79195250603531153.471035077341
Winsorized Mean ( 5 / 32 )121.5823958333330.780087809171097155.857320681019
Winsorized Mean ( 6 / 32 )121.5836458333330.77970663511191155.935117591865
Winsorized Mean ( 7 / 32 )121.5763541666670.776891087218112156.490859744584
Winsorized Mean ( 8 / 32 )121.5788541666670.776016578173878156.670434094032
Winsorized Mean ( 9 / 32 )121.5113541666670.763847064636192159.078118896144
Winsorized Mean ( 10 / 32 )121.5342708333330.7590934220178160.104497428359
Winsorized Mean ( 11 / 32 )121.5755208333330.752398589509198161.583929752764
Winsorized Mean ( 12 / 32 )121.5630208333330.74858183346842162.391091258644
Winsorized Mean ( 13 / 32 )121.5047916666670.741243368941179163.920240986747
Winsorized Mean ( 14 / 32 )121.4610416666670.733763990559208165.531483187258
Winsorized Mean ( 15 / 32 )121.4626041666670.730676840825762166.233001212133
Winsorized Mean ( 16 / 32 )121.45093750.71699124756282169.389707214465
Winsorized Mean ( 17 / 32 )121.38718750.707779371150661171.504274421924
Winsorized Mean ( 18 / 32 )121.47343750.691594851927968175.642483690223
Winsorized Mean ( 19 / 32 )121.4714583333330.69139653326423175.690002030876
Winsorized Mean ( 20 / 32 )121.4777083333330.686346040784839176.991926979608
Winsorized Mean ( 21 / 32 )121.4798958333330.682246715658004178.058601155991
Winsorized Mean ( 22 / 32 )121.55781250.670278781407686181.354110963666
Winsorized Mean ( 23 / 32 )121.5410416666670.667444926421863182.098982036228
Winsorized Mean ( 24 / 32 )121.5460416666670.663667036959527183.143104746483
Winsorized Mean ( 25 / 32 )121.5069791666670.657319302095802184.85229138906
Winsorized Mean ( 26 / 32 )121.5448958333330.638080471791978190.485214963542
Winsorized Mean ( 27 / 32 )121.8655208333330.586816079516949207.672429381366
Winsorized Mean ( 28 / 32 )121.88593750.572850436263518212.770960418595
Winsorized Mean ( 29 / 32 )122.076250.536931773288438227.358960808641
Winsorized Mean ( 30 / 32 )122.3481250.492802122856291248.270288063833
Winsorized Mean ( 31 / 32 )122.8938541666670.419289927373871293.099943841687
Winsorized Mean ( 32 / 32 )122.9205208333330.411898481408537298.424311769715
Trimmed Mean ( 1 / 32 )121.5891489361700.797701365651152152.424396110841
Trimmed Mean ( 2 / 32 )121.6192391304350.792196596516387153.521537034171
Trimmed Mean ( 3 / 32 )121.6485555555560.78622326996851154.725203644033
Trimmed Mean ( 4 / 32 )121.6814772727270.77961194798454156.079543915790
Trimmed Mean ( 5 / 32 )121.7204651162790.774597250400284157.140326864546
Trimmed Mean ( 6 / 32 )121.7520238095240.771775745964185157.755700987232
Trimmed Mean ( 7 / 32 )121.7848780487800.768263845211887158.519600795730
Trimmed Mean ( 8 / 32 )121.8206250.764448989608599159.357428233861
Trimmed Mean ( 9 / 32 )121.8578205128210.759843663211063160.372227094525
Trimmed Mean ( 10 / 32 )121.9064473684210.75628706848859161.190707137233
Trimmed Mean ( 11 / 32 )121.9547297297300.752539234118926162.057636599525
Trimmed Mean ( 12 / 32 )122.0006944444440.748837004564335162.920226565757
Trimmed Mean ( 13 / 32 )122.0507142857140.744598084408986163.914891592275
Trimmed Mean ( 14 / 32 )122.110.740164570125579164.976823977514
Trimmed Mean ( 15 / 32 )122.1774242424240.735439240829133166.128508596688
Trimmed Mean ( 16 / 32 )122.248906250.729689204509668167.535582950207
Trimmed Mean ( 17 / 32 )122.3261290322580.724246954955987168.901129918719
Trimmed Mean ( 18 / 32 )122.41450.718261925416366170.431559391149
Trimmed Mean ( 19 / 32 )122.5010344827590.712911164502834171.832116794226
Trimmed Mean ( 20 / 32 )122.5939285714290.705587655906037173.747269450182
Trimmed Mean ( 21 / 32 )122.6931481481480.696587259579036176.134642804542
Trimmed Mean ( 22 / 32 )122.7998076923080.685281068294566179.196264677084
Trimmed Mean ( 23 / 32 )122.90820.672628877871697182.728104670291
Trimmed Mean ( 24 / 32 )123.0270833333330.656231244806857187.475199187663
Trimmed Mean ( 25 / 32 )123.1558695652170.635158816617736193.897756502902
Trimmed Mean ( 26 / 32 )123.2997727272730.608053290670808202.777905520826
Trimmed Mean ( 27 / 32 )123.4540476190480.575963976032229214.343349161371
Trimmed Mean ( 28 / 32 )123.595250.546738345929985226.059230928404
Trimmed Mean ( 29 / 32 )123.7494736842110.509627781969179242.823248775897
Trimmed Mean ( 30 / 32 )123.9033333333330.468851010280739264.270163903758
Trimmed Mean ( 31 / 32 )124.0497058823530.426308928116061290.985474854003
Trimmed Mean ( 32 / 32 )124.16156250.394303210805354314.888540335250
Median124.895
Midrange119.98
Midmean - Weighted Average at Xnp122.808367346939
Midmean - Weighted Average at X(n+1)p123.027083333333
Midmean - Empirical Distribution Function122.808367346939
Midmean - Empirical Distribution Function - Averaging123.027083333333
Midmean - Empirical Distribution Function - Interpolation123.027083333333
Midmean - Closest Observation122.808367346939
Midmean - True Basic - Statistics Graphics Toolkit123.027083333333
Midmean - MS Excel (old versions)122.9082
Number of observations96
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/03/t1249290678vmfejd6bpiq3bll/1krgi1249290646.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/03/t1249290678vmfejd6bpiq3bll/1krgi1249290646.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/03/t1249290678vmfejd6bpiq3bll/2tfxu1249290646.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/03/t1249290678vmfejd6bpiq3bll/2tfxu1249290646.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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