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Eigen reeks , mediaan en rekenkundig gemiddelde

R Software Module: rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Mon, 21 Apr 2008 13:08:38 -0600
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Apr/21/t12088049718dai00shcfmykr0.htm/, Retrieved Mon, 21 Apr 2008 21:09:33 +0200
 
User-defined keywords:
Nicholas Van der Gucht
 
Dataseries X:
» Textbox « » Textfile « » CSV «
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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 time2 seconds
R Server'George Udny Yule' @ 72.249.76.132


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.42843750.00221798927532092193.164820392565
Geometric Mean0.427906364619015
Harmonic Mean0.427389723270719
Quadratic Mean0.428982565690806
Winsorized Mean ( 1 / 32 )0.42843750.00221798927532092193.164820392565
Winsorized Mean ( 2 / 32 )0.42843750.00221798927532092193.164820392565
Winsorized Mean ( 3 / 32 )0.42843750.00221798927532092193.164820392565
Winsorized Mean ( 4 / 32 )0.42843750.00221798927532092193.164820392565
Winsorized Mean ( 5 / 32 )0.42843750.00221798927532092193.164820392565
Winsorized Mean ( 6 / 32 )0.42843750.00221798927532092193.164820392565
Winsorized Mean ( 7 / 32 )0.42843750.00221798927532092193.164820392565
Winsorized Mean ( 8 / 32 )0.42843750.00221798927532092193.164820392565
Winsorized Mean ( 9 / 32 )0.42843750.00221798927532092193.164820392565
Winsorized Mean ( 10 / 32 )0.42843750.00221798927532092193.164820392565
Winsorized Mean ( 11 / 32 )0.4272916666666670.00200590775851546213.016607993429
Winsorized Mean ( 12 / 32 )0.4272916666666670.00200590775851546213.016607993429
Winsorized Mean ( 13 / 32 )0.4272916666666670.00200590775851546213.016607993429
Winsorized Mean ( 14 / 32 )0.4272916666666670.00200590775851546213.016607993429
Winsorized Mean ( 15 / 32 )0.4272916666666670.00200590775851546213.016607993429
Winsorized Mean ( 16 / 32 )0.4272916666666670.00200590775851546213.016607993429
Winsorized Mean ( 17 / 32 )0.4272916666666670.00200590775851546213.016607993429
Winsorized Mean ( 18 / 32 )0.4272916666666670.00200590775851546213.016607993429
Winsorized Mean ( 19 / 32 )0.42531250.00168164187860993252.915026326276
Winsorized Mean ( 20 / 32 )0.42531250.00168164187860993252.915026326276
Winsorized Mean ( 21 / 32 )0.4231250.00136780413725604309.346191077352
Winsorized Mean ( 22 / 32 )0.4231250.00136780413725604309.346191077352
Winsorized Mean ( 23 / 32 )0.4231250.00136780413725604309.346191077352
Winsorized Mean ( 24 / 32 )0.4231250.00136780413725604309.346191077352
Winsorized Mean ( 25 / 32 )0.4231250.00136780413725604309.346191077352
Winsorized Mean ( 26 / 32 )0.4231250.00136780413725604309.346191077352
Winsorized Mean ( 27 / 32 )0.4231250.00136780413725604309.346191077352
Winsorized Mean ( 28 / 32 )0.4231250.00136780413725604309.346191077352
Winsorized Mean ( 29 / 32 )0.4231250.00136780413725604309.346191077352
Winsorized Mean ( 30 / 32 )0.4231250.00136780413725604309.346191077352
Winsorized Mean ( 31 / 32 )0.4231250.00136780413725604309.346191077352
Winsorized Mean ( 32 / 32 )0.4231250.00136780413725604309.346191077352
Trimmed Mean ( 1 / 32 )0.4281914893617020.00221247666306637193.534917908808
Trimmed Mean ( 2 / 32 )0.4279347826086960.00220507408751823194.068210692335
Trimmed Mean ( 3 / 32 )0.4276666666666670.0021955010177864194.792288048155
Trimmed Mean ( 4 / 32 )0.4273863636363640.00218342716491254195.741067302093
Trimmed Mean ( 5 / 32 )0.4270930232558140.00216846115426554196.956732388629
Trimmed Mean ( 6 / 32 )0.4267857142857140.00215013584999377198.492441436643
Trimmed Mean ( 7 / 32 )0.4264634146341460.00212788905027575200.416189264606
Trimmed Mean ( 8 / 32 )0.4261250.00210103764297911202.816451872699
Trimmed Mean ( 9 / 32 )0.4257692307692310.00206874229045332205.81066705797
Trimmed Mean ( 10 / 32 )0.4253947368421050.00202995799346119209.558393923602
Trimmed Mean ( 11 / 32 )0.4250.00198336286362248214.282523785772
Trimmed Mean ( 12 / 32 )0.4247222222222220.00196777861282743215.838417723198
Trimmed Mean ( 13 / 32 )0.4244285714285710.00194793211250711217.886736762250
Trimmed Mean ( 14 / 32 )0.4241176470588240.00192295972533288220.554617692477
Trimmed Mean ( 15 / 32 )0.4237878787878790.00189177031968242224.016559715887
Trimmed Mean ( 16 / 32 )0.42343750.00185296242327347228.519205074838
Trimmed Mean ( 17 / 32 )0.4230645161290320.00180469904408924234.423860041737
Trimmed Mean ( 18 / 32 )0.4226666666666670.00174450981680861242.283914136917
Trimmed Mean ( 19 / 32 )0.4222413793103450.00166895976760520252.996739349937
Trimmed Mean ( 20 / 32 )0.4219642857142860.00163999609710382257.295908483843
Trimmed Mean ( 21 / 32 )0.4216666666666670.00160253991273471263.123971712567
Trimmed Mean ( 22 / 32 )0.4215384615384620.00161031309043206261.7742251759
Trimmed Mean ( 23 / 32 )0.42140.00161649658969322260.687218696808
Trimmed Mean ( 24 / 32 )0.421250.00162059550389172259.935313277376
Trimmed Mean ( 25 / 32 )0.4210869565217390.00162195864388402259.616333689856
Trimmed Mean ( 26 / 32 )0.4209090909090910.00161971801562029259.865659855551
Trimmed Mean ( 27 / 32 )0.4207142857142860.00161269848890840260.875971923964
Trimmed Mean ( 28 / 32 )0.42050.00159927868356091262.931035298818
Trimmed Mean ( 29 / 32 )0.4202631578947370.00157716827222967266.466911168968
Trimmed Mean ( 30 / 32 )0.420.00154303349962092272.19110933313
Trimmed Mean ( 31 / 32 )0.4197058823529410.0014918252657287281.337159246952
Trimmed Mean ( 32 / 32 )0.4193750.00141546042890872296.281684344455
Median0.42
Midrange0.44
Midmean - Weighted Average at Xnp0.418400000000001
Midmean - Weighted Average at X(n+1)p0.418400000000001
Midmean - Empirical Distribution Function0.418400000000001
Midmean - Empirical Distribution Function - Averaging0.418400000000001
Midmean - Empirical Distribution Function - Interpolation0.418400000000001
Midmean - Closest Observation0.418400000000001
Midmean - True Basic - Statistics Graphics Toolkit0.418400000000001
Midmean - MS Excel (old versions)0.418400000000001
Number of observations96
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t12088049718dai00shcfmykr0/1t4dr1208804916.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t12088049718dai00shcfmykr0/1t4dr1208804916.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t12088049718dai00shcfmykr0/2010x1208804916.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t12088049718dai00shcfmykr0/2010x1208804916.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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