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Maatstaven voor centrale tendentie

*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: Fri, 01 Oct 2010 07:49:55 +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/Oct/01/t1285919378z1x6glfxidfcd6i.htm/, Retrieved Fri, 01 Oct 2010 09:49:41 +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/2010/Oct/01/t1285919378z1x6glfxidfcd6i.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:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
426.113 383.703 232.444 70.939 226.731 947.293 611.281 158.047 217.465 1030.944 136.452 556.277 213.361 274.482 260.642 2763.544 213.923 169.861 403.064 406.167 206.893 156.187 257.102 62.156 662.883 251.422 171.328 350.089 221.588 183.186 190.379 223.166 232.669 356.725 109.215 315.955 278.741 207.533 192.797 601.162 289.714 293.671 386.688 131.812 197.549 308.174 242.205 238.502 187.881 140.321 421.403 218.761 1305.923 262.517 348.821 150.034 261.596 203.077 249.148 211.655 401.915 216.886 184.641 653.641 313.906 366.936 236.302 229.641 263.906 241.171 216.548 193.299 257.567 136.813 240.755 213.511 380.531 242.344 250.407 183.613 191.835 266.793 246.542 330.563 403.556 208.108 308.532 199.297 200.156 262.875 287.069 190.157 265.777 435.956 72.844 206.771 4202.361 401.422 216.046 441.437
 
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'George Udny Yule' @ 72.249.76.132


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean357.4579149.57324525372417.21070222799559
Geometric Mean270.707233435928
Harmonic Mean232.670487382683
Quadratic Mean609.154590621437
Winsorized Mean ( 1 / 33 )343.1575739.32476303869038.72624635175497
Winsorized Mean ( 2 / 33 )314.0432523.268716538762713.4963718122074
Winsorized Mean ( 3 / 33 )306.8850119.839662037767415.4682579479330
Winsorized Mean ( 4 / 33 )304.4428518.548099248467116.4136953291945
Winsorized Mean ( 5 / 33 )290.4543514.050994971623920.6714435943201
Winsorized Mean ( 6 / 33 )289.9214913.901077136918720.8560449772645
Winsorized Mean ( 7 / 33 )287.2018513.110882457308821.9056078746168
Winsorized Mean ( 8 / 33 )287.1693712.823748806273322.3935585715403
Winsorized Mean ( 9 / 33 )283.6834911.791221236101324.0588726408969
Winsorized Mean ( 10 / 33 )272.385499.3460001759894629.1446056998563
Winsorized Mean ( 11 / 33 )273.082129.0813248584055730.0707357415188
Winsorized Mean ( 12 / 33 )272.0778.8502396722782430.7423312898781
Winsorized Mean ( 13 / 33 )273.006248.5725647649296431.8465065573921
Winsorized Mean ( 14 / 33 )270.932988.20187990086933.0330342890408
Winsorized Mean ( 15 / 33 )270.695538.1203566377302933.3354238091274
Winsorized Mean ( 16 / 33 )271.135218.0525202398498233.6708511030153
Winsorized Mean ( 17 / 33 )271.32687.9801323737153834.0002881272602
Winsorized Mean ( 18 / 33 )271.278027.9613682861600334.0742960568207
Winsorized Mean ( 19 / 33 )268.75527.4784640176329235.9372191089403
Winsorized Mean ( 20 / 33 )268.35067.3637165069787636.4422774485788
Winsorized Mean ( 21 / 33 )267.78997.2477460274128536.9480248048358
Winsorized Mean ( 22 / 33 )265.7346.6872168426941339.7376077747976
Winsorized Mean ( 23 / 33 )263.787516.290834091033441.9320405184406
Winsorized Mean ( 24 / 33 )262.401036.0336477659477543.4896169247597
Winsorized Mean ( 25 / 33 )262.814285.9117643646245344.4561494319119
Winsorized Mean ( 26 / 33 )259.027645.12915860815250.5010002202536
Winsorized Mean ( 27 / 33 )255.116424.5826911091249155.6695648746694
Winsorized Mean ( 28 / 33 )254.72194.4869591316380356.7693826769958
Winsorized Mean ( 29 / 33 )253.330194.2633889020638759.4199112066377
Winsorized Mean ( 30 / 33 )254.286894.1368879284926361.4681602198141
Winsorized Mean ( 31 / 33 )250.319823.503247329780271.4536532639576
Winsorized Mean ( 32 / 33 )249.101583.341204348648974.5544282859355
Winsorized Mean ( 33 / 33 )248.364693.2199626828785377.1327852091661
Trimmed Mean ( 1 / 33 )321.23748979591831.32911151687910.2536418762737
Trimmed Mean ( 2 / 33 )298.40407291666718.885339891253415.8008314721871
Trimmed Mean ( 3 / 33 )290.08536170212815.792301351342018.3687833234944
Trimmed Mean ( 4 / 33 )283.99853260869613.803759542884920.5739988244784
Trimmed Mean ( 5 / 33 )278.31955555555611.873288793014523.4408141170878
Trimmed Mean ( 6 / 33 )275.56164772727311.200910925366924.6017176248766
Trimmed Mean ( 7 / 33 )272.77873255814010.446028601767926.1131519888787
Trimmed Mean ( 8 / 33 )270.3258214285719.7665624887897827.6787069901878
Trimmed Mean ( 9 / 33 )267.7582073170739.021421386316629.6802683137272
Trimmed Mean ( 10 / 33 )265.54636258.3862784862234831.6643864064644
Trimmed Mean ( 11 / 33 )264.6695512820518.1805498040241632.3535162822254
Trimmed Mean ( 12 / 33 )263.6632631578957.9860100398961633.0156438372476
Trimmed Mean ( 13 / 33 )262.715770270277.7986399915680733.6873827429295
Trimmed Mean ( 14 / 33 )261.6163611111117.6215943005413534.3256739725085
Trimmed Mean ( 15 / 33 )260.6656857142867.4753806604098934.869887910162
Trimmed Mean ( 16 / 33 )259.6823676470597.31283301143735.5105015034427
Trimmed Mean ( 17 / 33 )258.5978181818187.1261076544951336.2887891566857
Trimmed Mean ( 18 / 33 )257.4278756.9103651894697537.2524270341425
Trimmed Mean ( 19 / 33 )256.1868225806456.6493208710577838.5282689087451
Trimmed Mean ( 20 / 33 )255.0843333333336.4214218821906739.7239642579458
Trimmed Mean ( 21 / 33 )253.9406896551726.1605942887882841.220161197325
Trimmed Mean ( 22 / 33 )252.7630357142865.8579553592431843.1486790549632
Trimmed Mean ( 23 / 33 )251.6712037037045.593489323640744.9935968662752
Trimmed Mean ( 24 / 33 )250.6581346153855.3430936835915246.9125471981051
Trimmed Mean ( 25 / 33 )249.679565.0800199698434449.1493264755207
Trimmed Mean ( 26 / 33 )248.5854.7624345647112152.1970426306685
Trimmed Mean ( 27 / 33 )247.7118695652174.5398916179798454.5633883822637
Trimmed Mean ( 28 / 33 )247.0885909090914.3816101980205556.3921891136543
Trimmed Mean ( 29 / 33 )247.0885909090914.1931218686005458.9271188990166
Trimmed Mean ( 30 / 33 )245.8454753.9982186413239261.4887521305222
Trimmed Mean ( 31 / 33 )245.1053.7586414858756765.2110612094989
Trimmed Mean ( 32 / 33 )244.6377222222223.617517567581967.6258560330222
Trimmed Mean ( 33 / 33 )244.2274411764713.4664728705921170.4541619951446
Median242.2745
Midrange2132.2585
Midmean - Weighted Average at Xnp248.708509803922
Midmean - Weighted Average at X(n+1)p249.67956
Midmean - Empirical Distribution Function248.708509803922
Midmean - Empirical Distribution Function - Averaging249.67956
Midmean - Empirical Distribution Function - Interpolation249.67956
Midmean - Closest Observation248.708509803922
Midmean - True Basic - Statistics Graphics Toolkit249.67956
Midmean - MS Excel (old versions)250.658134615385
Number of observations100
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Oct/01/t1285919378z1x6glfxidfcd6i/17ngz1285919390.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Oct/01/t1285919378z1x6glfxidfcd6i/17ngz1285919390.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Oct/01/t1285919378z1x6glfxidfcd6i/2iexk1285919390.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Oct/01/t1285919378z1x6glfxidfcd6i/2iexk1285919390.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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