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Maarten Verhaegen 2MAR03 - tweede zit - Oefening 5.2 - Centrummaten evolutie prijzen diesel

R Software Module: rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Sun, 17 Aug 2008 07:43:10 -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/Aug/17/t1218980678bist1d3bej40pb1.htm/, Retrieved Sun, 17 Aug 2008 13:44:38 +0000
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
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Text written by user:
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.7633333333333330.012681720048629660.191624669701
Geometric Mean0.753788201775021
Harmonic Mean0.744659134798744
Quadratic Mean0.773276308960775
Winsorized Mean ( 1 / 32 )0.7632291666666670.012653872917698060.3158552034449
Winsorized Mean ( 2 / 32 )0.7630208333333330.012514132179388960.9727324592311
Winsorized Mean ( 3 / 32 )0.7633333333333330.012467208450559761.227285671883
Winsorized Mean ( 4 / 32 )0.76250.012263553189924462.176107380238
Winsorized Mean ( 5 / 32 )0.7619791666666670.012141002545082862.7608110481183
Winsorized Mean ( 6 / 32 )0.7601041666666670.011720890399072864.8503774701962
Winsorized Mean ( 7 / 32 )0.7586458333333330.011414844705111566.4613363503416
Winsorized Mean ( 8 / 32 )0.75781250.011247029944202667.3788994747563
Winsorized Mean ( 9 / 32 )0.7550.010393570887306972.6410593804714
Winsorized Mean ( 10 / 32 )0.7560416666666670.010233543878913073.8787731417803
Winsorized Mean ( 11 / 32 )0.753750.0098366594136959376.6266237652315
Winsorized Mean ( 12 / 32 )0.75250.0096313632417605878.1301650774876
Winsorized Mean ( 13 / 32 )0.7511458333333330.0094170778419002979.7642162403277
Winsorized Mean ( 14 / 32 )0.7526041666666670.0091912486882267881.882689958187
Winsorized Mean ( 15 / 32 )0.7510416666666670.0089497613006817983.917508124988
Winsorized Mean ( 16 / 32 )0.7510416666666670.0089497613006817983.917508124988
Winsorized Mean ( 17 / 32 )0.7510416666666670.0089497613006817983.917508124988
Winsorized Mean ( 18 / 32 )0.7547916666666670.0083901299138189989.9618568984832
Winsorized Mean ( 19 / 32 )0.75281250.0074951784574918100.439569820719
Winsorized Mean ( 20 / 32 )0.75281250.00628578025729363119.764368015646
Winsorized Mean ( 21 / 32 )0.7506250.00597291492650768125.671470167563
Winsorized Mean ( 22 / 32 )0.7552083333333330.00535162536112609141.117563800173
Winsorized Mean ( 23 / 32 )0.75281250.00435966139488725172.676827811181
Winsorized Mean ( 24 / 32 )0.75531250.00405270411404101186.372475943443
Winsorized Mean ( 25 / 32 )0.7527083333333330.00369173795028402203.889968212783
Winsorized Mean ( 26 / 32 )0.750.00333771641653287224.704530404378
Winsorized Mean ( 27 / 32 )0.75281250.00299745186008196251.150822478736
Winsorized Mean ( 28 / 32 )0.7498958333333330.00263035081905182285.093466583159
Winsorized Mean ( 29 / 32 )0.7498958333333330.00263035081905182285.093466583159
Winsorized Mean ( 30 / 32 )0.7498958333333330.00263035081905182285.093466583159
Winsorized Mean ( 31 / 32 )0.7531250.00226196865428822332.951121392523
Winsorized Mean ( 32 / 32 )0.7531250.00226196865428822332.951121392523
Trimmed Mean ( 1 / 32 )0.7619148936170210.012299433332504661.9471542321755
Trimmed Mean ( 2 / 32 )0.760543478260870.011893543690598763.9459103229294
Trimmed Mean ( 3 / 32 )0.7592222222222220.011513686994581065.9408426318657
Trimmed Mean ( 4 / 32 )0.7577272727272730.011095584604704268.2908832407101
Trimmed Mean ( 5 / 32 )0.756395348837210.010685035357622570.7901587145998
Trimmed Mean ( 6 / 32 )0.7551190476190480.010245822578512573.7001877431177
Trimmed Mean ( 7 / 32 )0.7541463414634150.0098512746765355376.553173698394
Trimmed Mean ( 8 / 32 )0.7533750.0094683746583500879.5675104951201
Trimmed Mean ( 9 / 32 )0.7526923076923080.0090594533794944883.0836338753043
Trimmed Mean ( 10 / 32 )0.7523684210526320.0087677007349296285.8113710536758
Trimmed Mean ( 11 / 32 )0.7518918918918920.0084567757298582488.9099954770227
Trimmed Mean ( 12 / 32 )0.7516666666666670.0081697560507038792.006011195635
Trimmed Mean ( 13 / 32 )0.7515714285714290.0078696305807623195.5027584660303
Trimmed Mean ( 14 / 32 )0.7516176470588240.0075531778604069499.5101215607187
Trimmed Mean ( 15 / 32 )0.7515151515151510.00721705576423487104.130434357926
Trimmed Mean ( 16 / 32 )0.75156250.00685818199075046109.586257846995
Trimmed Mean ( 17 / 32 )0.7516129032258060.00641914091520175117.089329110355
Trimmed Mean ( 18 / 32 )0.7516666666666670.00587134507860125128.022907290222
Trimmed Mean ( 19 / 32 )0.7513793103448280.00530639147003658141.598921713111
Trimmed Mean ( 20 / 32 )0.751250.00480166705358738156.456079027540
Trimmed Mean ( 21 / 32 )0.7511111111111110.00444444444444445169
Trimmed Mean ( 22 / 32 )0.7511538461538460.00406075510065179184.978859235633
Trimmed Mean ( 23 / 32 )0.75080.00371252705617847202.234216381131
Trimmed Mean ( 24 / 32 )0.7506250.00350286420292216214.28892372528
Trimmed Mean ( 25 / 32 )0.7502173913043480.00329674309248589227.563195025504
Trimmed Mean ( 26 / 32 )0.750.00311851864871254240.498802311037
Trimmed Mean ( 27 / 32 )0.750.00297101757186175252.438762767069
Trimmed Mean ( 28 / 32 )0.749750.00285296741602898262.796552034783
Trimmed Mean ( 29 / 32 )0.7497368421052630.00278399311307783269.302692806017
Trimmed Mean ( 30 / 32 )0.7497222222222220.002687009050354279.017378867202
Trimmed Mean ( 31 / 32 )0.7497058823529410.00255021910622924293.977047117907
Trimmed Mean ( 32 / 32 )0.7493750.00245678372884603305.022778847525
Median0.75
Midrange0.83
Midmean - Weighted Average at Xnp0.7508
Midmean - Weighted Average at X(n+1)p0.751836734693878
Midmean - Empirical Distribution Function0.7508
Midmean - Empirical Distribution Function - Averaging0.751836734693878
Midmean - Empirical Distribution Function - Interpolation0.751836734693878
Midmean - Closest Observation0.7508
Midmean - True Basic - Statistics Graphics Toolkit0.751836734693878
Midmean - MS Excel (old versions)0.7508
Number of observations96
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/17/t1218980678bist1d3bej40pb1/120jp1218980584.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/17/t1218980678bist1d3bej40pb1/120jp1218980584.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/17/t1218980678bist1d3bej40pb1/2gtsh1218980584.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/17/t1218980678bist1d3bej40pb1/2gtsh1218980584.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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