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verbetering opdracht 5

*Unverified author*
R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Thu, 09 Dec 2010 21:06:47 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/09/t1291929114adpzq7n6t8ppn4z.htm/, Retrieved Thu, 09 Dec 2010 22:11:55 +0100
 
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/2010/Dec/09/t1291929114adpzq7n6t8ppn4z.htm/},
    year = {2010},
}
@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 = {2010},
    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:
KDGP1W52 - Evi Van Dingenen
 
Dataseries X:
» Textbox « » Textfile « » CSV «
84,9 81,9 95,9 81 89,2 102,5 89,8 88,8 83,2 90,2 100,4 187,1 87,6 85,4 86,1 86,7 89,1 103,7 86,9 85,2 80,8 91,2 102,8 182,5 80,9 83,1 88,3 86,6 93 105,3 93,8 86,4 87 96,7 100,5 196,7 86,8 88,2 93,8 85 90,4 115,9 94,9 87,7 91,7 95,9 106,8 204,5 90,2 90,5 93,2 97,8 99,4 120 108,2 98,5 104,3 102,9 111,1 188,1 93,8 94,5 112,4 102,5 115,8 136,5 122,1 110,6 116,4 112,6 121,5 199,3 102,1 100,6 119 106,8 121,3 145,5 129,7 117,7 121,3 124,3 135,2 210,1 106,8 110,5 111,5 122,1 126,3 143,2 137,3 121,5 121,9 123,9 131,6 220,9
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean110.7927083333333.1711169945248334.9380702524143
Geometric Mean107.41167076504
Harmonic Mean104.739701535714
Quadratic Mean115.023226368272
Winsorized Mean ( 1 / 32 )110.681253.1316456748290435.3428393542773
Winsorized Mean ( 2 / 32 )110.5666666666673.0932916474807735.7440161701902
Winsorized Mean ( 3 / 32 )110.4322916666673.0395010897420536.3323744279488
Winsorized Mean ( 4 / 32 )110.3739583333333.0015683929448636.7720950796143
Winsorized Mean ( 5 / 32 )109.931252.8689498936587538.3175914793707
Winsorized Mean ( 6 / 32 )109.9752.8409092472089338.711197870205
Winsorized Mean ( 7 / 32 )109.6468752.7454363860478639.937867639993
Winsorized Mean ( 8 / 32 )106.5802083333331.9752540475024253.9577217766479
Winsorized Mean ( 9 / 32 )106.3833333333331.9290841083467655.1470684316116
Winsorized Mean ( 10 / 32 )105.8416666666671.8023362437881958.724706353464
Winsorized Mean ( 11 / 32 )105.7843751.7816470106195559.3744857255505
Winsorized Mean ( 12 / 32 )105.6468751.7495888947729260.3838280613413
Winsorized Mean ( 13 / 32 )105.1729166666671.6638648461466763.2100118649874
Winsorized Mean ( 14 / 32 )104.9104166666671.6166163488054864.895061060211
Winsorized Mean ( 15 / 32 )104.3947916666671.531819215570968.1508565798734
Winsorized Mean ( 16 / 32 )104.0781251.4807398008192670.287922930427
Winsorized Mean ( 17 / 32 )104.1135416666671.4578031265172571.418108366524
Winsorized Mean ( 18 / 32 )103.7947916666671.4083424450486473.6999669587334
Winsorized Mean ( 19 / 32 )103.893751.3965369233534374.3938439884033
Winsorized Mean ( 20 / 32 )103.8729166666671.3883684094208574.8165371394446
Winsorized Mean ( 21 / 32 )103.8947916666671.3636126310055576.1908399088774
Winsorized Mean ( 22 / 32 )103.9635416666671.355639714168576.6896547660041
Winsorized Mean ( 23 / 32 )103.9395833333331.3463624475889877.200298864147
Winsorized Mean ( 24 / 32 )104.0895833333331.3292314749365578.3080940347897
Winsorized Mean ( 25 / 32 )103.8552083333331.2717509943571581.663162674255
Winsorized Mean ( 26 / 32 )103.5843751.2358704299287983.8149149712795
Winsorized Mean ( 27 / 32 )103.2751.181939196049487.377591288278
Winsorized Mean ( 28 / 32 )102.9251.1304235737723991.0499412680538
Winsorized Mean ( 29 / 32 )102.9854166666671.0872032557094194.7250811895955
Winsorized Mean ( 30 / 32 )103.1104166666671.0655690753362196.765586627158
Winsorized Mean ( 31 / 32 )102.4968750.891700835291796114.945361654236
Winsorized Mean ( 32 / 32 )102.4968750.876300353466007116.965461208131
Trimmed Mean ( 1 / 32 )109.9404255319152.9988769800540936.6605320135312
Trimmed Mean ( 2 / 32 )109.1673913043482.8434391119744638.3927304244412
Trimmed Mean ( 3 / 32 )108.4211111111112.685258454953440.3764155033607
Trimmed Mean ( 4 / 32 )107.6897727272732.5233393515755742.6774831772156
Trimmed Mean ( 5 / 32 )106.9406976744192.3442413523810545.6184673842558
Trimmed Mean ( 6 / 32 )106.2571428571432.1750081842581748.8536749545077
Trimmed Mean ( 7 / 32 )105.5317073170731.9764999054105453.3932265962609
Trimmed Mean ( 8 / 32 )104.826251.7593257336785459.5831959899891
Trimmed Mean ( 9 / 32 )104.556410256411.707781830435361.2235171923336
Trimmed Mean ( 10 / 32 )104.31.6570593272526762.9428278665945
Trimmed Mean ( 11 / 32 )104.11.6229175988834664.1437372246252
Trimmed Mean ( 12 / 32 )103.8958333333331.5862074698235265.499523429235
Trimmed Mean ( 13 / 32 )103.6957142857141.5484025505159366.9694804178426
Trimmed Mean ( 14 / 32 )103.5352941176471.5188973010050368.1647758865195
Trimmed Mean ( 15 / 32 )103.3924242424241.491616526780769.3156869651828
Trimmed Mean ( 16 / 32 )103.29218751.4729291770323170.1270564197224
Trimmed Mean ( 17 / 32 )103.2161290322581.4580674995172770.7896781640292
Trimmed Mean ( 18 / 32 )103.1316666666671.4427169356144971.4843391110125
Trimmed Mean ( 19 / 32 )103.0706896551721.4310234950270272.0258542318525
Trimmed Mean ( 20 / 32 )102.9964285714291.4172590252711172.6729741951905
Trimmed Mean ( 21 / 32 )102.9185185185191.4004219042672873.4910802272596
Trimmed Mean ( 22 / 32 )102.8326923076921.3823813834266974.3880766484191
Trimmed Mean ( 23 / 32 )102.7341.3598277501963675.5492745203689
Trimmed Mean ( 24 / 32 )102.6291666666671.3318884846634977.0553750170735
Trimmed Mean ( 25 / 32 )102.5021739130431.2980940659901378.9635948569407
Trimmed Mean ( 26 / 32 )102.3840909090911.2654789731640380.9054066327978
Trimmed Mean ( 27 / 32 )102.2785714285711.2299284499660383.1581474771125
Trimmed Mean ( 28 / 32 )102.191.1944519180843585.5538832939305
Trimmed Mean ( 29 / 32 )102.1236842105261.1584707767959888.1538716867536
Trimmed Mean ( 30 / 32 )102.0444444444441.1189524894835191.1964050337353
Trimmed Mean ( 31 / 32 )101.9441176470591.0685188173535895.406946505206
Trimmed Mean ( 32 / 32 )101.8906251.046974898940897.3190714534613
Median102.3
Midrange150.85
Midmean - Weighted Average at Xnp102.734
Midmean - Weighted Average at X(n+1)p103.010204081633
Midmean - Empirical Distribution Function102.734
Midmean - Empirical Distribution Function - Averaging103.010204081633
Midmean - Empirical Distribution Function - Interpolation103.010204081633
Midmean - Closest Observation102.734
Midmean - True Basic - Statistics Graphics Toolkit103.010204081633
Midmean - MS Excel (old versions)102.734
Number of observations96
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/09/t1291929114adpzq7n6t8ppn4z/18sc61291928803.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t1291929114adpzq7n6t8ppn4z/18sc61291928803.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t1291929114adpzq7n6t8ppn4z/2j2t91291928803.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t1291929114adpzq7n6t8ppn4z/2j2t91291928803.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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