Home » date » 2011 » Apr » 03 »

Isabelle Regnard oef 5/2 Koffie, thee, cacao: centrummaten

*Unverified author*
R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Sun, 03 Apr 2011 15:35:37 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Apr/03/t13018447956fogo4wxr5ur595.htm/, Retrieved Sun, 03 Apr 2011 17:33:18 +0200
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
KDGP1W52
 
Dataseries X:
» Textbox « » Textfile « » CSV «
106,42 106,22 106,32 105,81 105,92 107,54 107,34 107,24 107,74 105,71 105,41 106,22 106,32 106,12 106,22 105,92 105,71 105,71 105,92 105,71 105,41 104,49 101,35 99,72 99,01 97,89 95,86 94,95 95,35 95,15 95,46 95,56 95,05 94,64 93,63 93,12 93,53 97,18 96,27 95,15 97,08 101,95 103,07 103,68 102,87 102,56 103,38 103,27 102,89 102,69 101,54 102,9 101,53 101,96 101,99 101,11 101,75 101,71 104,11 103,57 103,32 103,64 103,68 103,79 103,01 101,54 101,9 103,68 104,62 104,11 105,04 104,83 105,05 104,68 107,32 109,9 109,77 110,69 110,54 110,89 110,95 109,73 110,85 110,39 110,58 110,4 111,07 110,86 111,38 111,44 110,36 110,06 108,34 107,94 107,39 107,1 107,61 107,74 106,9 106,71 106,6 108,21 110,54 110,91 109,51 110,27 111,39 112,13 111,64
 
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'George Udny Yule' @ 216.218.223.82


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean104.5954128440370.472355084723042221.433866654287
Geometric Mean104.477721466207
Harmonic Mean104.357498206876
Quadratic Mean104.710540420864
Winsorized Mean ( 1 / 36 )104.5946788990830.470879404596599222.126255423485
Winsorized Mean ( 2 / 36 )104.5928440366970.469979921125734222.547473488161
Winsorized Mean ( 3 / 36 )104.6192660550460.464022959861537225.461399768373
Winsorized Mean ( 4 / 36 )104.6302752293580.461736433982413226.601731050192
Winsorized Mean ( 5 / 36 )104.6206422018350.458960756267795227.951171800821
Winsorized Mean ( 6 / 36 )104.6195412844040.457048014939266228.902736396975
Winsorized Mean ( 7 / 36 )104.6169724770640.456719427158723229.061796490445
Winsorized Mean ( 8 / 36 )104.6301834862390.453733389574768230.598377572116
Winsorized Mean ( 9 / 36 )104.6367889908260.451702876866327231.649596116677
Winsorized Mean ( 10 / 36 )104.645045871560.449865114073731232.61427169569
Winsorized Mean ( 11 / 36 )104.6591743119270.442194376881909236.681377655502
Winsorized Mean ( 12 / 36 )104.6922018348620.432437173354756242.098062529367
Winsorized Mean ( 13 / 36 )104.7840366972480.414804444451477252.610689443819
Winsorized Mean ( 14 / 36 )104.7968807339450.412602311723134253.990047453409
Winsorized Mean ( 15 / 36 )104.8753211009170.393725995041017266.366260856086
Winsorized Mean ( 16 / 36 )105.0382568807340.367508274332658285.811950959386
Winsorized Mean ( 17 / 36 )105.1443119266050.350516810976265299.969384160937
Winsorized Mean ( 18 / 36 )105.3589908256880.317661748551183331.670373616647
Winsorized Mean ( 19 / 36 )105.3642201834860.307330484550834342.836866110034
Winsorized Mean ( 20 / 36 )105.3678899082570.299236259496619352.122734342117
Winsorized Mean ( 21 / 36 )105.3447706422020.29551436398124356.479357629091
Winsorized Mean ( 22 / 36 )105.3366972477060.294396878095274357.805075682959
Winsorized Mean ( 23 / 36 )105.3261467889910.283761591204956371.178306203237
Winsorized Mean ( 24 / 36 )105.0773394495410.24938339325183421.348583317387
Winsorized Mean ( 25 / 36 )105.0819266055050.241566114167184435.002760911984
Winsorized Mean ( 26 / 36 )105.0294495412840.232511762984814451.716713997581
Winsorized Mean ( 27 / 36 )104.9823853211010.226542918305178463.410580681575
Winsorized Mean ( 28 / 36 )104.9900917431190.225592454239197465.397178718564
Winsorized Mean ( 29 / 36 )105.1071559633030.203520079838419516.446121909693
Winsorized Mean ( 30 / 36 )105.1236697247710.197212509009084533.047676605182
Winsorized Mean ( 31 / 36 )105.1322018348620.186602779486896563.401049673245
Winsorized Mean ( 32 / 36 )105.1233944954130.184304222833487570.379738886333
Winsorized Mean ( 33 / 36 )105.1203669724770.18329102127828573.516183386194
Winsorized Mean ( 34 / 36 )105.1297247706420.176694382585203594.980571722184
Winsorized Mean ( 35 / 36 )105.1040366972480.169619365567243619.646443940863
Winsorized Mean ( 36 / 36 )105.1040366972480.155195727663214677.23537419362
Trimmed Mean ( 1 / 36 )104.6322429906540.463626773405843225.682055033225
Trimmed Mean ( 2 / 36 )104.6712380952380.455474668785718229.806936078989
Trimmed Mean ( 3 / 36 )104.7127184466020.446822872624888234.349503711528
Trimmed Mean ( 4 / 36 )104.7463366336630.439550867144375238.303105427064
Trimmed Mean ( 5 / 36 )104.7782828282830.432079844437055242.497501740206
Trimmed Mean ( 6 / 36 )104.8137113402060.424363843667729246.990201696528
Trimmed Mean ( 7 / 36 )104.8508421052630.416051957065197252.01381780505
Trimmed Mean ( 8 / 36 )104.890.406643894165388257.940673658165
Trimmed Mean ( 9 / 36 )104.9289010989010.396514806112469264.627952049636
Trimmed Mean ( 10 / 36 )104.9686516853930.38529631192489272.436170387885
Trimmed Mean ( 11 / 36 )105.0091954022990.372725185057755281.733565672594
Trimmed Mean ( 12 / 36 )105.050.359603929336705292.126952544057
Trimmed Mean ( 13 / 36 )105.0891566265060.346153974902578303.590784003224
Trimmed Mean ( 14 / 36 )105.1207407407410.333697337259942315.018218616633
Trimmed Mean ( 15 / 36 )105.1526582278480.319512860957824329.103053669343
Trimmed Mean ( 16 / 36 )105.1788311688310.306217077632574343.478005805522
Trimmed Mean ( 17 / 36 )105.19160.295159937709759356.38847472396
Trimmed Mean ( 18 / 36 )105.1957534246580.284980634192656369.132989414087
Trimmed Mean ( 19 / 36 )105.1818309859150.278109984313066378.202282977058
Trimmed Mean ( 20 / 36 )105.1666666666670.271520509954487387.32494530264
Trimmed Mean ( 21 / 36 )105.1502985074630.264883679457822396.967826491575
Trimmed Mean ( 22 / 36 )105.1347692307690.257517186477643408.263116993541
Trimmed Mean ( 23 / 36 )105.1188888888890.248815124666347422.477890079432
Trimmed Mean ( 24 / 36 )105.1027868852460.240046799984765437.842899350945
Trimmed Mean ( 25 / 36 )105.1047457627120.235122654230863447.020922362978
Trimmed Mean ( 26 / 36 )105.106491228070.230277223582809456.434594758232
Trimmed Mean ( 27 / 36 )105.1123636363640.225682647724477465.752970803008
Trimmed Mean ( 28 / 36 )105.1222641509430.220849830030469475.989789697553
Trimmed Mean ( 29 / 36 )105.1323529411760.214890868469993489.236018681069
Trimmed Mean ( 30 / 36 )105.1342857142860.211286752629536497.590522859827
Trimmed Mean ( 31 / 36 )105.1351063829790.207665512456616506.271383915722
Trimmed Mean ( 32 / 36 )105.1353333333330.204767569638743513.437423312765
Trimmed Mean ( 33 / 36 )105.1362790697670.201212829603081522.512800387344
Trimmed Mean ( 34 / 36 )105.137560975610.196538887261096534.945335453831
Trimmed Mean ( 35 / 36 )105.1382051282050.191595288637763548.751516155406
Trimmed Mean ( 36 / 36 )105.1410810810810.186391280045082564.087982311461
Median105.41
Midrange102.625
Midmean - Weighted Average at Xnp105.112363636364
Midmean - Weighted Average at X(n+1)p105.112363636364
Midmean - Empirical Distribution Function105.112363636364
Midmean - Empirical Distribution Function - Averaging105.112363636364
Midmean - Empirical Distribution Function - Interpolation105.112363636364
Midmean - Closest Observation105.055892857143
Midmean - True Basic - Statistics Graphics Toolkit105.112363636364
Midmean - MS Excel (old versions)105.112363636364
Number of observations109
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2011/Apr/03/t13018447956fogo4wxr5ur595/1u9mi1301844934.png (open in new window)
http://www.freestatistics.org/blog/date/2011/Apr/03/t13018447956fogo4wxr5ur595/1u9mi1301844934.ps (open in new window)


http://www.freestatistics.org/blog/date/2011/Apr/03/t13018447956fogo4wxr5ur595/2le1a1301844934.png (open in new window)
http://www.freestatistics.org/blog/date/2011/Apr/03/t13018447956fogo4wxr5ur595/2le1a1301844934.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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